On solving system of differential-algebraic equations using adomian decomposition method

On solving system of differential-algebraic... | F1000Research "use strict";function _typeof(t){return(_typeof="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(t){return typeof t}:function(t){return t&&"function"==typeof Symbol&&t.constructor===Symbol&&t!==Symbol.prototype?"symbol":typeof t})(t)}!function(){var t=function(){var t,e,o=[],n=window,r=n;for(;r;){try{if(r.frames.__tcfapiLocator){t=r;break}}catch(t){}if(r===n.top)break;r=r.parent}t||(!function t(){var e=n.document,o=!!n.frames.__tcfapiLocator;if(!o)if(e.body){var r=e.createElement("iframe");r.style.cssText="display:none",r.name="__tcfapiLocator",e.body.appendChild(r)}else setTimeout(t,5);return!o}(),n.__tcfapi=function(){for(var t=arguments.length,n=new Array(t),r=0;r 3&&2===parseInt(n[1],10)&&"boolean"==typeof n[3]&&(e=n[3],"function"==typeof n[2]&&n[2]("set",!0)):"ping"===n[0]?"function"==typeof n[2]&&n[2]({gdprApplies:e,cmpLoaded:!1,cmpStatus:"stub"}):o.push(n)},n.addEventListener("message",(function(t){var e="string"==typeof t.data,o={};if(e)try{o=JSON.parse(t.data)}catch(t){}else o=t.data;var n="object"===_typeof(o)&&null!==o?o.__tcfapiCall:null;n&&window.__tcfapi(n.command,n.version,(function(o,r){var a={__tcfapiReturn:{returnValue:o,success:r,callId:n.callId}};t&&t.source&&t.source.postMessage&&t.source.postMessage(e?JSON.stringify(a):a,"*")}),n.parameter)}),!1))};"undefined"!=typeof module?module.exports=t:t()}(); dataLayer = dataLayer || []; // Standard GTM initialization - Google Consent Mode handles consent automatically (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl+ '>m_auth=hzk0Vc3qFsQYhCrIoHz68A>m_preview=env-1>m_cookies_win=x';f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-MWFK8L5J'); ;window.NREUM||(NREUM={});NREUM.init={distributed_tracing:{enabled:true},privacy:{cookies_enabled:true},ajax:{deny_list:["bam.nr-data.net"]}}; ;NREUM.loader_config={accountID:"438030",trustKey:"438030",agentID:"772317073",licenseKey:"97f8f67f26",applicationID:"772317073"} ;NREUM.info={beacon:"bam.nr-data.net",errorBeacon:"bam.nr-data.net",licenseKey:"97f8f67f26",applicationID:"772317073",sa:1} ;/*! For license information please see nr-loader-spa-1.236.0.min.js.LICENSE.txt */ (()=>{"use strict";var e,t,r={5763:(e,t,r)=>{r.d(t,{P_:()=>l,Mt:()=>g,C5:()=>s,DL:()=>v,OP:()=>T,lF:()=>D,Yu:()=>y,Dg:()=>h,CX:()=>c,GE:()=>b,sU:()=>_});var n=r(8632),i=r(9567);const o={beacon:n.ce.beacon,errorBeacon:n.ce.errorBeacon,licenseKey:void 0,applicationID:void 0,sa:void 0,queueTime:void 0,applicationTime:void 0,ttGuid:void 0,user:void 0,account:void 0,product:void 0,extra:void 0,jsAttributes:{},userAttributes:void 0,atts:void 0,transactionName:void 0,tNamePlain:void 0},a={};function s(e){if(!e)throw new Error("All info objects require an agent identifier!");if(!a[e])throw new Error("Info for ".concat(e," was never set"));return a[e]}function c(e,t){if(!e)throw new Error("All info objects require an agent identifier!");a[e]=(0,i.D)(t,o),(0,n.Qy)(e,a[e],"info")}var u=r(7056);const d=()=>{const e={blockSelector:"[data-nr-block]",maskInputOptions:{password:!0}};return{allow_bfcache:!0,privacy:{cookies_enabled:!0},ajax:{deny_list:void 0,enabled:!0,harvestTimeSeconds:10},distributed_tracing:{enabled:void 0,exclude_newrelic_header:void 0,cors_use_newrelic_header:void 0,cors_use_tracecontext_headers:void 0,allowed_origins:void 0},session:{domain:void 0,expiresMs:u.oD,inactiveMs:u.Hb},ssl:void 0,obfuscate:void 0,jserrors:{enabled:!0,harvestTimeSeconds:10},metrics:{enabled:!0},page_action:{enabled:!0,harvestTimeSeconds:30},page_view_event:{enabled:!0},page_view_timing:{enabled:!0,harvestTimeSeconds:30,long_task:!1},session_trace:{enabled:!0,harvestTimeSeconds:10},harvest:{tooManyRequestsDelay:60},session_replay:{enabled:!1,harvestTimeSeconds:60,sampleRate:.1,errorSampleRate:.1,maskTextSelector:"*",maskAllInputs:!0,get blockClass(){return"nr-block"},get ignoreClass(){return"nr-ignore"},get maskTextClass(){return"nr-mask"},get blockSelector(){return e.blockSelector},set blockSelector(t){e.blockSelector+=",".concat(t)},get maskInputOptions(){return e.maskInputOptions},set maskInputOptions(t){e.maskInputOptions={...t,password:!0}}},spa:{enabled:!0,harvestTimeSeconds:10}}},f={};function l(e){if(!e)throw new Error("All configuration objects require an agent identifier!");if(!f[e])throw new Error("Configuration for ".concat(e," was never set"));return f[e]}function h(e,t){if(!e)throw new Error("All configuration objects require an agent identifier!");f[e]=(0,i.D)(t,d()),(0,n.Qy)(e,f[e],"config")}function g(e,t){if(!e)throw new Error("All configuration objects require an agent identifier!");var r=l(e);if(r){for(var n=t.split("."),i=0;i {r.d(t,{D:()=>i});var n=r(50);function i(e,t){try{if(!e||"object"!=typeof e)return(0,n.Z)("Setting a Configurable requires an object as input");if(!t||"object"!=typeof t)return(0,n.Z)("Setting a Configurable requires a model to set its initial properties");const r=Object.create(Object.getPrototypeOf(t),Object.getOwnPropertyDescriptors(t)),o=0===Object.keys(r).length?e:r;for(let a in o)if(void 0!==e[a])try{"object"==typeof e[a]&&"object"==typeof t[a]?r[a]=i(e[a],t[a]):r[a]=e[a]}catch(e){(0,n.Z)("An error occurred while setting a property of a Configurable",e)}return r}catch(e){(0,n.Z)("An error occured while setting a Configurable",e)}}},6818:(e,t,r)=>{r.d(t,{Re:()=>i,gF:()=>o,q4:()=>n});const n="1.236.0",i="PROD",o="CDN"},385:(e,t,r)=>{r.d(t,{FN:()=>a,IF:()=>u,Nk:()=>f,Tt:()=>s,_A:()=>o,il:()=>n,pL:()=>c,v6:()=>i,w1:()=>d});const n="undefined"!=typeof window&&!!window.document,i="undefined"!=typeof WorkerGlobalScope&&("undefined"!=typeof self&&self instanceof WorkerGlobalScope&&self.navigator instanceof WorkerNavigator||"undefined"!=typeof globalThis&&globalThis instanceof WorkerGlobalScope&&globalThis.navigator instanceof WorkerNavigator),o=n?window:"undefined"!=typeof WorkerGlobalScope&&("undefined"!=typeof self&&self instanceof WorkerGlobalScope&&self||"undefined"!=typeof globalThis&&globalThis instanceof WorkerGlobalScope&&globalThis),a=""+o?.location,s=/iPad|iPhone|iPod/.test(navigator.userAgent),c=s&&"undefined"==typeof SharedWorker,u=(()=>{const e=navigator.userAgent.match(/Firefox[/\s](\d+\.\d+)/);return Array.isArray(e)&&e.length>=2?+e[1]:0})(),d=Boolean(n&&window.document.documentMode),f=!!navigator.sendBeacon},1117:(e,t,r)=>{r.d(t,{w:()=>o});var n=r(50);const i={agentIdentifier:"",ee:void 0};class o{constructor(e){try{if("object"!=typeof e)return(0,n.Z)("shared context requires an object as input");this.sharedContext={},Object.assign(this.sharedContext,i),Object.entries(e).forEach((e=>{let[t,r]=e;Object.keys(i).includes(t)&&(this.sharedContext[t]=r)}))}catch(e){(0,n.Z)("An error occured while setting SharedContext",e)}}}},8e3:(e,t,r)=>{r.d(t,{L:()=>d,R:()=>c});var n=r(2177),i=r(1284),o=r(4322),a=r(3325);const s={};function c(e,t){const r={staged:!1,priority:a.p[t]||0};u(e),s[e].get(t)||s[e].set(t,r)}function u(e){e&&(s[e]||(s[e]=new Map))}function d(){let e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:"",t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:"feature";if(u(e),!e||!s[e].get(t))return a(t);s[e].get(t).staged=!0;const r=[...s[e]];function a(t){const r=e?n.ee.get(e):n.ee,a=o.X.handlers;if(r.backlog&&a){var s=r.backlog[t],c=a[t];if(c){for(var u=0;s&&u {let[t,r]=e;return r.staged}))&&(r.sort(((e,t)=>e[1].priority-t[1].priority)),r.forEach((e=>{let[t]=e;a(t)})))}function f(e,t){var r=e[1];(0,i.D)(t[r],(function(t,r){var n=e[0];if(r[0]===n){var i=r[1],o=e[3],a=e[2];i.apply(o,a)}}))}},2177:(e,t,r)=>{r.d(t,{c:()=>f,ee:()=>u});var n=r(8632),i=r(2210),o=r(1284),a=r(5763),s="nr@context";let c=(0,n.fP)();var u;function d(){}function f(e){return(0,i.X)(e,s,l)}function l(){return new d}function h(){u.aborted=!0,u.backlog={}}c.ee?u=c.ee:(u=function e(t,r){var n={},c={},f={},g=!1;try{g=16===r.length&&(0,a.OP)(r).isolatedBacklog}catch(e){}var p={on:b,addEventListener:b,removeEventListener:y,emit:v,get:x,listeners:w,context:m,buffer:A,abort:h,aborted:!1,isBuffering:E,debugId:r,backlog:g?{}:t&&"object"==typeof t.backlog?t.backlog:{}};return p;function m(e){return e&&e instanceof d?e:e?(0,i.X)(e,s,l):l()}function v(e,r,n,i,o){if(!1!==o&&(o=!0),!u.aborted||i){t&&o&&t.emit(e,r,n);for(var a=m(n),s=w(e),d=s.length,f=0;fn,p:()=>i});var n=r(2177).ee.get("handle");function i(e,t,r,i,o){o?(o.buffer([e],i),o.emit(e,t,r)):(n.buffer([e],i),n.emit(e,t,r))}},4322:(e,t,r)=>{r.d(t,{X:()=>o});var n=r(5546);o.on=a;var i=o.handlers={};function o(e,t,r,o){a(o||n.E,i,e,t,r)}function a(e,t,r,i,o){o||(o="feature"),e||(e=n.E);var a=t[o]=t[o]||{};(a[r]=a[r]||[]).push([e,i])}},3239:(e,t,r)=>{r.d(t,{bP:()=>s,iz:()=>c,m$:()=>a});var n=r(385);let i=!1,o=!1;try{const e={get passive(){return i=!0,!1},get signal(){return o=!0,!1}};n._A.addEventListener("test",null,e),n._A.removeEventListener("test",null,e)}catch(e){}function a(e,t){return i||o?{capture:!!e,passive:i,signal:t}:!!e}function s(e,t){let r=arguments.length>2&&void 0!==arguments[2]&&arguments[2],n=arguments.length>3?arguments[3]:void 0;window.addEventListener(e,t,a(r,n))}function c(e,t){let r=arguments.length>2&&void 0!==arguments[2]&&arguments[2],n=arguments.length>3?arguments[3]:void 0;document.addEventListener(e,t,a(r,n))}},4402:(e,t,r)=>{r.d(t,{Ht:()=>u,M:()=>c,Rl:()=>a,ky:()=>s});var n=r(385);const i="xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx";function o(e,t){return e?15&e[t]:16*Math.random()|0}function a(){const e=n._A?.crypto||n._A?.msCrypto;let t,r=0;return e&&e.getRandomValues&&(t=e.getRandomValues(new Uint8Array(31))),i.split("").map((e=>"x"===e?o(t,++r).toString(16):"y"===e?(3&o()|8).toString(16):e)).join("")}function s(e){const t=n._A?.crypto||n._A?.msCrypto;let r,i=0;t&&t.getRandomValues&&(r=t.getRandomValues(new Uint8Array(31)));const a=[];for(var s=0;s {r.d(t,{Bq:()=>n,Hb:()=>o,oD:()=>i});const n="NRBA",i=144e5,o=18e5},7894:(e,t,r)=>{function n(){return Math.round(performance.now())}r.d(t,{z:()=>n})},7243:(e,t,r)=>{r.d(t,{e:()=>o});var n=r(385),i={};function o(e){if(e in i)return i[e];if(0===(e||"").indexOf("data:"))return{protocol:"data"};let t;var r=n._A?.location,o={};if(n.il)t=document.createElement("a"),t.href=e;else try{t=new URL(e,r.href)}catch(e){return o}o.port=t.port;var a=t.href.split("://");!o.port&&a[1]&&(o.port=a[1].split("/")[0].split("@").pop().split(":")[1]),o.port&&"0"!==o.port||(o.port="https"===a[0]?"443":"80"),o.hostname=t.hostname||r.hostname,o.pathname=t.pathname,o.protocol=a[0],"/"!==o.pathname.charAt(0)&&(o.pathname="/"+o.pathname);var s=!t.protocol||":"===t.protocol||t.protocol===r.protocol,c=t.hostname===r.hostname&&t.port===r.port;return o.sameOrigin=s&&(!t.hostname||c),"/"===o.pathname&&(i[e]=o),o}},50:(e,t,r)=>{function n(e,t){"function"==typeof console.warn&&(console.warn("New Relic: ".concat(e)),t&&console.warn(t))}r.d(t,{Z:()=>n})},2587:(e,t,r)=>{r.d(t,{N:()=>c,T:()=>u});var n=r(2177),i=r(5546),o=r(8e3),a=r(3325);const s={stn:[a.D.sessionTrace],err:[a.D.jserrors,a.D.metrics],ins:[a.D.pageAction],spa:[a.D.spa],sr:[a.D.sessionReplay,a.D.sessionTrace]};function c(e,t){const r=n.ee.get(t);e&&"object"==typeof e&&(Object.entries(e).forEach((e=>{let[t,n]=e;void 0===u[t]&&(s[t]?s[t].forEach((e=>{n?(0,i.p)("feat-"+t,[],void 0,e,r):(0,i.p)("block-"+t,[],void 0,e,r),(0,i.p)("rumresp-"+t,[Boolean(n)],void 0,e,r)})):n&&(0,i.p)("feat-"+t,[],void 0,void 0,r),u[t]=Boolean(n))})),Object.keys(s).forEach((e=>{void 0===u[e]&&(s[e]?.forEach((t=>(0,i.p)("rumresp-"+e,[!1],void 0,t,r))),u[e]=!1)})),(0,o.L)(t,a.D.pageViewEvent))}const u={}},2210:(e,t,r)=>{r.d(t,{X:()=>i});var n=Object.prototype.hasOwnProperty;function i(e,t,r){if(n.call(e,t))return e[t];var i=r();if(Object.defineProperty&&Object.keys)try{return Object.defineProperty(e,t,{value:i,writable:!0,enumerable:!1}),i}catch(e){}return e[t]=i,i}},1284:(e,t,r)=>{r.d(t,{D:()=>n});const n=(e,t)=>Object.entries(e||{}).map((e=>{let[r,n]=e;return t(r,n)}))},4351:(e,t,r)=>{r.d(t,{P:()=>o});var n=r(2177);const i=()=>{const e=new WeakSet;return(t,r)=>{if("object"==typeof r&&null!==r){if(e.has(r))return;e.add(r)}return r}};function o(e){try{return JSON.stringify(e,i())}catch(e){try{n.ee.emit("internal-error",[e])}catch(e){}}}},3960:(e,t,r)=>{r.d(t,{K:()=>a,b:()=>o});var n=r(3239);function i(){return"undefined"==typeof document||"complete"===document.readyState}function o(e,t){if(i())return e();(0,n.bP)("load",e,t)}function a(e){if(i())return e();(0,n.iz)("DOMContentLoaded",e)}},8632:(e,t,r)=>{r.d(t,{EZ:()=>u,Qy:()=>c,ce:()=>o,fP:()=>a,gG:()=>d,mF:()=>s});var n=r(7894),i=r(385);const o={beacon:"bam.nr-data.net",errorBeacon:"bam.nr-data.net"};function a(){return i._A.NREUM||(i._A.NREUM={}),void 0===i._A.newrelic&&(i._A.newrelic=i._A.NREUM),i._A.NREUM}function s(){let e=a();return e.o||(e.o={ST:i._A.setTimeout,SI:i._A.setImmediate,CT:i._A.clearTimeout,XHR:i._A.XMLHttpRequest,REQ:i._A.Request,EV:i._A.Event,PR:i._A.Promise,MO:i._A.MutationObserver,FETCH:i._A.fetch}),e}function c(e,t,r){let i=a();const o=i.initializedAgents||{},s=o[e]||{};return Object.keys(s).length||(s.initializedAt={ms:(0,n.z)(),date:new Date}),i.initializedAgents={...o,[e]:{...s,[r]:t}},i}function u(e,t){a()[e]=t}function d(){return function(){let e=a();const t=e.info||{};e.info={beacon:o.beacon,errorBeacon:o.errorBeacon,...t}}(),function(){let e=a();const t=e.init||{};e.init={...t}}(),s(),function(){let e=a();const t=e.loader_config||{};e.loader_config={...t}}(),a()}},7956:(e,t,r)=>{r.d(t,{N:()=>i});var n=r(3239);function i(e){let t=arguments.length>1&&void 0!==arguments[1]&&arguments[1],r=arguments.length>2?arguments[2]:void 0,i=arguments.length>3?arguments[3]:void 0;return void(0,n.iz)("visibilitychange",(function(){if(t)return void("hidden"==document.visibilityState&&e());e(document.visibilityState)}),r,i)}},1214:(e,t,r)=>{r.d(t,{em:()=>v,u5:()=>N,QU:()=>S,_L:()=>I,Gm:()=>L,Lg:()=>M,gy:()=>U,BV:()=>Q,Kf:()=>ee});var n=r(2177);const i="nr@original";var o=Object.prototype.hasOwnProperty,a=!1;function s(e,t){return e||(e=n.ee),r.inPlace=function(e,t,n,i,o){n||(n="");var a,s,c,u="-"===n.charAt(0);for(c=0;c 2?n-2:0),o=2;o {r(A[T],e,w),r(E[T],e,w)})),r(l._A,"fetch",y),t.on(y+"end",(function(e,r){var n=this;if(r){var i=r.headers.get("content-length");null!==i&&(n.rxSize=i),t.emit(y+"done",[null,r],n)}else t.emit(y+"done",[e],n)})),t}const O={},j=["pushState","replaceState"];function S(e){const t=function(e){return(e||n.ee).get("history")}(e);return!l.il||O[t.debugId]++||(O[t.debugId]=1,s(t).inPlace(window.history,j,"-")),t}var P=r(3239);const C={},R=["appendChild","insertBefore","replaceChild"];function I(e){const t=function(e){return(e||n.ee).get("jsonp")}(e);if(!l.il||C[t.debugId])return t;C[t.debugId]=!0;var r=s(t),i=/[?&](?:callback|cb)=([^&#]+)/,o=/(.*)\.([^.]+)/,a=/^(\w+)(\.|$)(.*)$/;function c(e,t){var r=e.match(a),n=r[1],i=r[3];return i?c(i,t[n]):t[n]}return r.inPlace(Node.prototype,R,"dom-"),t.on("dom-start",(function(e){!function(e){if(!e||"string"!=typeof e.nodeName||"script"!==e.nodeName.toLowerCase())return;if("function"!=typeof e.addEventListener)return;var n=(a=e.src,s=a.match(i),s?s[1]:null);var a,s;if(!n)return;var u=function(e){var t=e.match(o);if(t&&t.length>=3)return{key:t[2],parent:c(t[1],window)};return{key:e,parent:window}}(n);if("function"!=typeof u.parent[u.key])return;var d={};function f(){t.emit("jsonp-end",[],d),e.removeEventListener("load",f,(0,P.m$)(!1)),e.removeEventListener("error",l,(0,P.m$)(!1))}function l(){t.emit("jsonp-error",[],d),t.emit("jsonp-end",[],d),e.removeEventListener("load",f,(0,P.m$)(!1)),e.removeEventListener("error",l,(0,P.m$)(!1))}r.inPlace(u.parent,[u.key],"cb-",d),e.addEventListener("load",f,(0,P.m$)(!1)),e.addEventListener("error",l,(0,P.m$)(!1)),t.emit("new-jsonp",[e.src],d)}(e[0])})),t}var k=r(5763);const H={};function L(e){const t=function(e){return(e||n.ee).get("mutation")}(e);if(!l.il||H[t.debugId])return t;H[t.debugId]=!0;var r=s(t),i=k.Yu.MO;return i&&(window.MutationObserver=function(e){return this instanceof i?new i(r(e,"fn-")):i.apply(this,arguments)},MutationObserver.prototype=i.prototype),t}const z={};function M(e){const t=function(e){return(e||n.ee).get("promise")}(e);if(z[t.debugId])return t;z[t.debugId]=!0;var r=n.c,o=s(t),a=k.Yu.PR;return a&&function(){function e(r){var n=t.context(),i=o(r,"executor-",n,null,!1);const s=Reflect.construct(a,[i],e);return t.context(s).getCtx=function(){return n},s}l._A.Promise=e,Object.defineProperty(e,"name",{value:"Promise"}),e.toString=function(){return a.toString()},Object.setPrototypeOf(e,a),["all","race"].forEach((function(r){const n=a[r];e[r]=function(e){let i=!1;[...e||[]].forEach((e=>{this.resolve(e).then(a("all"===r),a(!1))}));const o=n.apply(this,arguments);return o;function a(e){return function(){t.emit("propagate",[null,!i],o,!1,!1),i=i||!e}}}})),["resolve","reject"].forEach((function(r){const n=a[r];e[r]=function(e){const r=n.apply(this,arguments);return e!==r&&t.emit("propagate",[e,!0],r,!1,!1),r}})),e.prototype=a.prototype;const n=a.prototype.then;a.prototype.then=function(){var e=this,i=r(e);i.promise=e;for(var a=arguments.length,s=new Array(a),c=0;c e())),t};function m(e,t){i.inPlace(t,["onreadystatechange"],"fn-",E)}function b(){var e=this,t=r.context(e);e.readyState>3&&!t.resolved&&(t.resolved=!0,r.emit("xhr-resolved",[],e)),i.inPlace(e,f,"fn-",E)}if(function(e,t){for(var r in e)t[r]=e[r]}(o,p),p.prototype=o.prototype,i.inPlace(p.prototype,J,"-xhr-",E),r.on("send-xhr-start",(function(e,t){m(e,t),function(e){h.push(e),a&&(y?y.then(A):u?u(A):(w=-w,x.data=w))}(t)})),r.on("open-xhr-start",m),a){var y=c&&c.resolve();if(!u&&!c){var w=1,x=document.createTextNode(w);new a(A).observe(x,{characterData:!0})}}else t.on("fn-end",(function(e){e[0]&&e[0].type===d||A()}));function A(){for(var e=0;e {r.d(t,{t:()=>n});const n=r(3325).D.ajax},6660:(e,t,r)=>{r.d(t,{A:()=>i,t:()=>n});const n=r(3325).D.jserrors,i="nr@seenError"},3081:(e,t,r)=>{r.d(t,{gF:()=>o,mY:()=>i,t9:()=>n,vz:()=>s,xS:()=>a});const n=r(3325).D.metrics,i="sm",o="cm",a="storeSupportabilityMetrics",s="storeEventMetrics"},4649:(e,t,r)=>{r.d(t,{t:()=>n});const n=r(3325).D.pageAction},7633:(e,t,r)=>{r.d(t,{Dz:()=>i,OJ:()=>a,qw:()=>o,t9:()=>n});const n=r(3325).D.pageViewEvent,i="firstbyte",o="domcontent",a="windowload"},9251:(e,t,r)=>{r.d(t,{t:()=>n});const n=r(3325).D.pageViewTiming},3614:(e,t,r)=>{r.d(t,{BST_RESOURCE:()=>i,END:()=>s,FEATURE_NAME:()=>n,FN_END:()=>u,FN_START:()=>c,PUSH_STATE:()=>d,RESOURCE:()=>o,START:()=>a});const n=r(3325).D.sessionTrace,i="bstResource",o="resource",a="-start",s="-end",c="fn"+a,u="fn"+s,d="pushState"},7836:(e,t,r)=>{r.d(t,{BODY:()=>A,CB_END:()=>E,CB_START:()=>u,END:()=>x,FEATURE_NAME:()=>i,FETCH:()=>_,FETCH_BODY:()=>v,FETCH_DONE:()=>m,FETCH_START:()=>p,FN_END:()=>c,FN_START:()=>s,INTERACTION:()=>l,INTERACTION_API:()=>d,INTERACTION_EVENTS:()=>o,JSONP_END:()=>b,JSONP_NODE:()=>g,JS_TIME:()=>T,MAX_TIMER_BUDGET:()=>a,REMAINING:()=>f,SPA_NODE:()=>h,START:()=>w,originalSetTimeout:()=>y});var n=r(5763);const i=r(3325).D.spa,o=["click","submit","keypress","keydown","keyup","change"],a=999,s="fn-start",c="fn-end",u="cb-start",d="api-ixn-",f="remaining",l="interaction",h="spaNode",g="jsonpNode",p="fetch-start",m="fetch-done",v="fetch-body-",b="jsonp-end",y=n.Yu.ST,w="-start",x="-end",A="-body",E="cb"+x,T="jsTime",_="fetch"},5938:(e,t,r)=>{r.d(t,{W:()=>o});var n=r(5763),i=r(2177);class o{constructor(e,t,r){this.agentIdentifier=e,this.aggregator=t,this.ee=i.ee.get(e,(0,n.OP)(this.agentIdentifier).isolatedBacklog),this.featureName=r,this.blocked=!1}}},9144:(e,t,r)=>{r.d(t,{j:()=>m});var n=r(3325),i=r(5763),o=r(5546),a=r(2177),s=r(7894),c=r(8e3),u=r(3960),d=r(385),f=r(50),l=r(3081),h=r(8632);function g(){const e=(0,h.gG)();["setErrorHandler","finished","addToTrace","inlineHit","addRelease","addPageAction","setCurrentRouteName","setPageViewName","setCustomAttribute","interaction","noticeError","setUserId"].forEach((t=>{e[t]=function(){for(var r=arguments.length,n=new Array(r),i=0;i 1?r-1:0),i=1;i {e.exposed&&e.api[t]&&o.push(e.api[t](...n))})),o.length>1?o:o[0]}(t,...n)}}))}var p=r(2587);function m(e){let t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:{},m=arguments.length>2?arguments[2]:void 0,v=arguments.length>3?arguments[3]:void 0,{init:b,info:y,loader_config:w,runtime:x={loaderType:m},exposed:A=!0}=t;const E=(0,h.gG)();y||(b=E.init,y=E.info,w=E.loader_config),(0,i.Dg)(e,b||{}),(0,i.GE)(e,w||{}),(0,i.sU)(e,x),y.jsAttributes??={},d.v6&&(y.jsAttributes.isWorker=!0),(0,i.CX)(e,y),g();const T=function(e,t){t||(0,c.R)(e,"api");const h={};var g=a.ee.get(e),p=g.get("tracer"),m="api-",v=m+"ixn-";function b(t,r,n,o){const a=(0,i.C5)(e);return null===r?delete a.jsAttributes[t]:(0,i.CX)(e,{...a,jsAttributes:{...a.jsAttributes,[t]:r}}),x(m,n,!0,o||null===r?"session":void 0)(t,r)}function y(){}["setErrorHandler","finished","addToTrace","inlineHit","addRelease"].forEach((e=>h[e]=x(m,e,!0,"api"))),h.addPageAction=x(m,"addPageAction",!0,n.D.pageAction),h.setCurrentRouteName=x(m,"routeName",!0,n.D.spa),h.setPageViewName=function(t,r){if("string"==typeof t)return"/"!==t.charAt(0)&&(t="/"+t),(0,i.OP)(e).customTransaction=(r||"http://custom.transaction")+t,x(m,"setPageViewName",!0)()},h.setCustomAttribute=function(e,t){let r=arguments.length>2&&void 0!==arguments[2]&&arguments[2];if("string"==typeof e){if(["string","number"].includes(typeof t)||null===t)return b(e,t,"setCustomAttribute",r);(0,f.Z)("Failed to execute setCustomAttribute.\nNon-null value must be a string or number type, but a type of was provided."))}else(0,f.Z)("Failed to execute setCustomAttribute.\nName must be a string type, but a type of was provided."))},h.setUserId=function(e){if("string"==typeof e||null===e)return b("enduser.id",e,"setUserId",!0);(0,f.Z)("Failed to execute setUserId.\nNon-null value must be a string type, but a type of was provided."))},h.interaction=function(){return(new y).get()};var w=y.prototype={createTracer:function(e,t){var r={},i=this,a="function"==typeof t;return(0,o.p)(v+"tracer",[(0,s.z)(),e,r],i,n.D.spa,g),function(){if(p.emit((a?"":"no-")+"fn-start",[(0,s.z)(),i,a],r),a)try{return t.apply(this,arguments)}catch(e){throw p.emit("fn-err",[arguments,this,"string"==typeof e?new Error(e):e],r),e}finally{p.emit("fn-end",[(0,s.z)()],r)}}}};function x(e,t,r,i){return function(){return(0,o.p)(l.xS,["API/"+t+"/called"],void 0,n.D.metrics,g),i&&(0,o.p)(e+t,[(0,s.z)(),...arguments],r?null:this,i,g),r?void 0:this}}function A(){r.e(439).then(r.bind(r,7438)).then((t=>{let{setAPI:r}=t;r(e),(0,c.L)(e,"api")})).catch((()=>(0,f.Z)("Downloading runtime APIs failed...")))}return["actionText","setName","setAttribute","save","ignore","onEnd","getContext","end","get"].forEach((e=>{w[e]=x(v,e,void 0,n.D.spa)})),h.noticeError=function(e,t){"string"==typeof e&&(e=new Error(e)),(0,o.p)(l.xS,["API/noticeError/called"],void 0,n.D.metrics,g),(0,o.p)("err",[e,(0,s.z)(),!1,t],void 0,n.D.jserrors,g)},d.il?(0,u.b)((()=>A()),!0):A(),h}(e,v);return(0,h.Qy)(e,T,"api"),(0,h.Qy)(e,A,"exposed"),(0,h.EZ)("activatedFeatures",p.T),T}},3325:(e,t,r)=>{r.d(t,{D:()=>n,p:()=>i});const n={ajax:"ajax",jserrors:"jserrors",metrics:"metrics",pageAction:"page_action",pageViewEvent:"page_view_event",pageViewTiming:"page_view_timing",sessionReplay:"session_replay",sessionTrace:"session_trace",spa:"spa"},i={[n.pageViewEvent]:1,[n.pageViewTiming]:2,[n.metrics]:3,[n.jserrors]:4,[n.ajax]:5,[n.sessionTrace]:6,[n.pageAction]:7,[n.spa]:8,[n.sessionReplay]:9}}},n={};function i(e){var t=n[e];if(void 0!==t)return t.exports;var o=n[e]={exports:{}};return r[e](o,o.exports,i),o.exports}i.m=r,i.d=(e,t)=>{for(var r in t)i.o(t,r)&&!i.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},i.f={},i.e=e=>Promise.all(Object.keys(i.f).reduce(((t,r)=>(i.f[r](e,t),t)),[])),i.u=e=>(({78:"page_action-aggregate",147:"metrics-aggregate",242:"session-manager",317:"jserrors-aggregate",348:"page_view_timing-aggregate",412:"lazy-feature-loader",439:"async-api",538:"recorder",590:"session_replay-aggregate",675:"compressor",733:"session_trace-aggregate",786:"page_view_event-aggregate",873:"spa-aggregate",898:"ajax-aggregate"}[e]||e)+"."+{78:"ac76d497",147:"3dc53903",148:"1a20d5fe",242:"2a64278a",317:"49e41428",348:"bd6de33a",412:"2f55ce66",439:"30bd804e",538:"1b18459f",590:"cf0efb30",675:"ae9f91a8",733:"83105561",786:"06482edd",860:"03a8b7a5",873:"e6b09d52",898:"998ef92b"}[e]+"-1.236.0.min.js"),i.o=(e,t)=>Object.prototype.hasOwnProperty.call(e,t),e={},t="NRBA:",i.l=(r,n,o,a)=>{if(e[r])e[r].push(n);else{var s,c;if(void 0!==o)for(var u=document.getElementsByTagName("script"),d=0;d {s.onerror=s.onload=null,clearTimeout(h);var i=e[r];if(delete e[r],s.parentNode&&s.parentNode.removeChild(s),i&&i.forEach((e=>e(n))),t)return t(n)},h=setTimeout(l.bind(null,void 0,{type:"timeout",target:s}),12e4);s.onerror=l.bind(null,s.onerror),s.onload=l.bind(null,s.onload),c&&document.head.appendChild(s)}},i.r=e=>{"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(e,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(e,"__esModule",{value:!0})},i.j=364,i.p="https://js-agent.newrelic.com/",(()=>{var e={364:0,953:0};i.f.j=(t,r)=>{var n=i.o(e,t)?e[t]:void 0;if(0!==n)if(n)r.push(n[2]);else{var o=new Promise(((r,i)=>n=e[t]=[r,i]));r.push(n[2]=o);var a=i.p+i.u(t),s=new Error;i.l(a,(r=>{if(i.o(e,t)&&(0!==(n=e[t])&&(e[t]=void 0),n)){var o=r&&("load"===r.type?"missing":r.type),a=r&&r.target&&r.target.src;s.message="Loading chunk "+t+" failed.\n("+o+": "+a+")",s.name="ChunkLoadError",s.type=o,s.request=a,n[1](s)}}),"chunk-"+t,t)}};var t=(t,r)=>{var n,o,[a,s,c]=r,u=0;if(a.some((t=>0!==e[t]))){for(n in s)i.o(s,n)&&(i.m[n]=s[n]);if(c)c(i)}for(t&&t(r);u {i.r(o);var e=i(3325),t=i(5763);const r=Object.values(e.D);function n(e){const n={};return r.forEach((r=>{n[r]=function(e,r){return!1!==(0,t.Mt)(r,"".concat(e,".enabled"))}(r,e)})),n}var a=i(9144);var s=i(5546),c=i(385),u=i(8e3),d=i(5938),f=i(3960),l=i(50);class h extends d.W{constructor(e,t,r){let n=!(arguments.length>3&&void 0!==arguments[3])||arguments[3];super(e,t,r),this.auto=n,this.abortHandler,this.featAggregate,this.onAggregateImported,n&&(0,u.R)(e,r)}importAggregator(){let e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};if(this.featAggregate||!this.auto)return;const r=c.il&&!0===(0,t.Mt)(this.agentIdentifier,"privacy.cookies_enabled");let n;this.onAggregateImported=new Promise((e=>{n=e}));const o=async()=>{let t;try{if(r){const{setupAgentSession:e}=await Promise.all([i.e(860),i.e(242)]).then(i.bind(i,3228));t=e(this.agentIdentifier)}}catch(e){(0,l.Z)("A problem occurred when starting up session manager. This page will not start or extend any session.",e)}try{if(!this.shouldImportAgg(this.featureName,t))return void(0,u.L)(this.agentIdentifier,this.featureName);const{lazyFeatureLoader:r}=await i.e(412).then(i.bind(i,8582)),{Aggregate:o}=await r(this.featureName,"aggregate");this.featAggregate=new o(this.agentIdentifier,this.aggregator,e),n(!0)}catch(e){(0,l.Z)("Downloading and initializing ".concat(this.featureName," failed..."),e),this.abortHandler?.(),n(!1)}};c.il?(0,f.b)((()=>o()),!0):o()}shouldImportAgg(r,n){return r!==e.D.sessionReplay||!1!==(0,t.Mt)(this.agentIdentifier,"session_trace.enabled")&&(!!n?.isNew||!!n?.state.sessionReplay)}}var g=i(7633),p=i(7894);class m extends h{static featureName=g.t9;constructor(r,n){let i=!(arguments.length>2&&void 0!==arguments[2])||arguments[2];if(super(r,n,g.t9,i),("undefined"==typeof PerformanceNavigationTiming||c.Tt)&&"undefined"!=typeof PerformanceTiming){const n=(0,t.OP)(r);n[g.Dz]=Math.max(Date.now()-n.offset,0),(0,f.K)((()=>n[g.qw]=Math.max((0,p.z)()-n[g.Dz],0))),(0,f.b)((()=>{const t=(0,p.z)();n[g.OJ]=Math.max(t-n[g.Dz],0),(0,s.p)("timing",["load",t],void 0,e.D.pageViewTiming,this.ee)}))}this.importAggregator()}}var v=i(1117),b=i(1284);class y extends v.w{constructor(e){super(e),this.aggregatedData={}}store(e,t,r,n,i){var o=this.getBucket(e,t,r,i);return o.metrics=function(e,t){t||(t={count:0});return t.count+=1,(0,b.D)(e,(function(e,r){t[e]=w(r,t[e])})),t}(n,o.metrics),o}merge(e,t,r,n,i){var o=this.getBucket(e,t,n,i);if(o.metrics){var a=o.metrics;a.count+=r.count,(0,b.D)(r,(function(e,t){if("count"!==e){var n=a[e],i=r[e];i&&!i.c?a[e]=w(i.t,n):a[e]=function(e,t){if(!t)return e;t.c||(t=x(t.t));return t.min=Math.min(e.min,t.min),t.max=Math.max(e.max,t.max),t.t+=e.t,t.sos+=e.sos,t.c+=e.c,t}(i,a[e])}}))}else o.metrics=r}storeMetric(e,t,r,n){var i=this.getBucket(e,t,r);return i.stats=w(n,i.stats),i}getBucket(e,t,r,n){this.aggregatedData[e]||(this.aggregatedData[e]={});var i=this.aggregatedData[e][t];return i||(i=this.aggregatedData[e][t]={params:r||{}},n&&(i.custom=n)),i}get(e,t){return t?this.aggregatedData[e]&&this.aggregatedData[e][t]:this.aggregatedData[e]}take(e){for(var t={},r="",n=!1,i=0;i t.max&&(t.max=e),e 2&&void 0!==arguments[2])||arguments[2];super(e,r,j.t,n),c.il&&((0,t.OP)(e).initHidden=Boolean("hidden"===document.visibilityState),(0,N.N)((()=>(0,s.p)("docHidden",[(0,p.z)()],void 0,j.t,this.ee)),!0),(0,O.bP)("pagehide",(()=>(0,s.p)("winPagehide",[(0,p.z)()],void 0,j.t,this.ee))),this.importAggregator())}}var P=i(3081);class C extends h{static featureName=P.t9;constructor(e,t){let r=!(arguments.length>2&&void 0!==arguments[2])||arguments[2];super(e,t,P.t9,r),this.importAggregator()}}var R,I=i(2210),k=i(1214),H=i(2177),L={};try{R=localStorage.getItem("__nr_flags").split(","),console&&"function"==typeof console.log&&(L.console=!0,-1!==R.indexOf("dev")&&(L.dev=!0),-1!==R.indexOf("nr_dev")&&(L.nrDev=!0))}catch(e){}function z(e){try{L.console&&z(e)}catch(e){}}L.nrDev&&H.ee.on("internal-error",(function(e){z(e.stack)})),L.dev&&H.ee.on("fn-err",(function(e,t,r){z(r.stack)})),L.dev&&(z("NR AGENT IN DEVELOPMENT MODE"),z("flags: "+(0,b.D)(L,(function(e,t){return e})).join(", ")));var M=i(6660);class B extends h{static featureName=M.t;constructor(r,n){let i=!(arguments.length>2&&void 0!==arguments[2])||arguments[2];super(r,n,M.t,i),this.skipNext=0;try{this.removeOnAbort=new AbortController}catch(e){}const o=this;o.ee.on("fn-start",(function(e,t,r){o.abortHandler&&(o.skipNext+=1)})),o.ee.on("fn-err",(function(t,r,n){o.abortHandler&&!n[M.A]&&((0,I.X)(n,M.A,(function(){return!0})),this.thrown=!0,(0,s.p)("err",[n,(0,p.z)()],void 0,e.D.jserrors,o.ee))})),o.ee.on("fn-end",(function(){o.abortHandler&&!this.thrown&&o.skipNext>0&&(o.skipNext-=1)})),o.ee.on("internal-error",(function(t){(0,s.p)("ierr",[t,(0,p.z)(),!0],void 0,e.D.jserrors,o.ee)})),this.origOnerror=c._A.onerror,c._A.onerror=this.onerrorHandler.bind(this),c._A.addEventListener("unhandledrejection",(t=>{const r=function(e){let t="Unhandled Promise Rejection: ";if(e instanceof Error)try{return e.message=t+e.message,e}catch(t){return e}if(void 0===e)return new Error(t);try{return new Error(t+(0,D.P)(e))}catch(e){return new Error(t)}}(t.reason);(0,s.p)("err",[r,(0,p.z)(),!1,{unhandledPromiseRejection:1}],void 0,e.D.jserrors,this.ee)}),(0,O.m$)(!1,this.removeOnAbort?.signal)),(0,k.gy)(this.ee),(0,k.BV)(this.ee),(0,k.em)(this.ee),(0,t.OP)(r).xhrWrappable&&(0,k.Kf)(this.ee),this.abortHandler=this.#e,this.importAggregator()}#e(){this.removeOnAbort?.abort(),this.abortHandler=void 0}onerrorHandler(t,r,n,i,o){"function"==typeof this.origOnerror&&this.origOnerror(...arguments);try{this.skipNext?this.skipNext-=1:(0,s.p)("err",[o||new F(t,r,n),(0,p.z)()],void 0,e.D.jserrors,this.ee)}catch(t){try{(0,s.p)("ierr",[t,(0,p.z)(),!0],void 0,e.D.jserrors,this.ee)}catch(e){}}return!1}}function F(e,t,r){this.message=e||"Uncaught error with no additional information",this.sourceURL=t,this.line=r}let U=1;const q="nr@id";function G(e){const t=typeof e;return!e||"object"!==t&&"function"!==t?-1:e===c._A?0:(0,I.X)(e,q,(function(){return U++}))}function V(e){if("string"==typeof e&&e.length)return e.length;if("object"==typeof e){if("undefined"!=typeof ArrayBuffer&&e instanceof ArrayBuffer&&e.byteLength)return e.byteLength;if("undefined"!=typeof Blob&&e instanceof Blob&&e.size)return e.size;if(!("undefined"!=typeof FormData&&e instanceof FormData))try{return(0,D.P)(e).length}catch(e){return}}}var X=i(7243);class W{constructor(e){this.agentIdentifier=e,this.generateTracePayload=this.generateTracePayload.bind(this),this.shouldGenerateTrace=this.shouldGenerateTrace.bind(this)}generateTracePayload(e){if(!this.shouldGenerateTrace(e))return null;var r=(0,t.DL)(this.agentIdentifier);if(!r)return null;var n=(r.accountID||"").toString()||null,i=(r.agentID||"").toString()||null,o=(r.trustKey||"").toString()||null;if(!n||!i)return null;var a=(0,_.M)(),s=(0,_.Ht)(),c=Date.now(),u={spanId:a,traceId:s,timestamp:c};return(e.sameOrigin||this.isAllowedOrigin(e)&&this.useTraceContextHeadersForCors())&&(u.traceContextParentHeader=this.generateTraceContextParentHeader(a,s),u.traceContextStateHeader=this.generateTraceContextStateHeader(a,c,n,i,o)),(e.sameOrigin&&!this.excludeNewrelicHeader()||!e.sameOrigin&&this.isAllowedOrigin(e)&&this.useNewrelicHeaderForCors())&&(u.newrelicHeader=this.generateTraceHeader(a,s,c,n,i,o)),u}generateTraceContextParentHeader(e,t){return"00-"+t+"-"+e+"-01"}generateTraceContextStateHeader(e,t,r,n,i){return i+"@nr=0-1-"+r+"-"+n+"-"+e+"----"+t}generateTraceHeader(e,t,r,n,i,o){if(!("function"==typeof c._A?.btoa))return null;var a={v:[0,1],d:{ty:"Browser",ac:n,ap:i,id:e,tr:t,ti:r}};return o&&n!==o&&(a.d.tk=o),btoa((0,D.P)(a))}shouldGenerateTrace(e){return this.isDtEnabled()&&this.isAllowedOrigin(e)}isAllowedOrigin(e){var r=!1,n={};if((0,t.Mt)(this.agentIdentifier,"distributed_tracing")&&(n=(0,t.P_)(this.agentIdentifier).distributed_tracing),e.sameOrigin)r=!0;else if(n.allowed_origins instanceof Array)for(var i=0;i 2&&void 0!==arguments[2])||arguments[2];super(r,n,Z.t,i),(0,t.OP)(r).xhrWrappable&&(this.dt=new W(r),this.handler=(e,t,r,n)=>(0,s.p)(e,t,r,n,this.ee),(0,k.u5)(this.ee),(0,k.Kf)(this.ee),function(r,n,i,o){function a(e){var t=this;t.totalCbs=0,t.called=0,t.cbTime=0,t.end=E,t.ended=!1,t.xhrGuids={},t.lastSize=null,t.loadCaptureCalled=!1,t.params=this.params||{},t.metrics=this.metrics||{},e.addEventListener("load",(function(r){_(t,e)}),(0,O.m$)(!1)),c.IF||e.addEventListener("progress",(function(e){t.lastSize=e.loaded}),(0,O.m$)(!1))}function s(e){this.params={method:e[0]},T(this,e[1]),this.metrics={}}function u(e,n){var i=(0,t.DL)(r);i.xpid&&this.sameOrigin&&n.setRequestHeader("X-NewRelic-ID",i.xpid);var a=o.generateTracePayload(this.parsedOrigin);if(a){var s=!1;a.newrelicHeader&&(n.setRequestHeader("newrelic",a.newrelicHeader),s=!0),a.traceContextParentHeader&&(n.setRequestHeader("traceparent",a.traceContextParentHeader),a.traceContextStateHeader&&n.setRequestHeader("tracestate",a.traceContextStateHeader),s=!0),s&&(this.dt=a)}}function d(e,t){var r=this.metrics,i=e[0],o=this;if(r&&i){var a=V(i);a&&(r.txSize=a)}this.startTime=(0,p.z)(),this.listener=function(e){try{"abort"!==e.type||o.loadCaptureCalled||(o.params.aborted=!0),("load"!==e.type||o.called===o.totalCbs&&(o.onloadCalled||"function"!=typeof t.onload)&&"function"==typeof o.end)&&o.end(t)}catch(e){try{n.emit("internal-error",[e])}catch(e){}}};for(var s=0;s 1?e[1]=i:e.push(i)}else e[0]&&e[0].headers&&s(e[0].headers,n)&&(this.dt=n);function s(e,t){var r=!1;return t.newrelicHeader&&(e.set("newrelic",t.newrelicHeader),r=!0),t.traceContextParentHeader&&(e.set("traceparent",t.traceContextParentHeader),t.traceContextStateHeader&&e.set("tracestate",t.traceContextStateHeader),r=!0),r}}function x(e,t){this.params={},this.metrics={},this.startTime=(0,p.z)(),this.dt=t,e.length>=1&&(this.target=e[0]),e.length>=2&&(this.opts=e[1]);var r,n=this.opts||{},i=this.target;"string"==typeof i?r=i:"object"==typeof i&&i instanceof Y?r=i.url:c._A?.URL&&"object"==typeof i&&i instanceof URL&&(r=i.href),T(this,r);var o=(""+(i&&i instanceof Y&&i.method||n.method||"GET")).toUpperCase();this.params.method=o,this.txSize=V(n.body)||0}function A(t,r){var n;this.endTime=(0,p.z)(),this.params||(this.params={}),this.params.status=r?r.status:0,"string"==typeof this.rxSize&&this.rxSize.length>0&&(n=+this.rxSize);var o={txSize:this.txSize,rxSize:n,duration:(0,p.z)()-this.startTime};i("xhr",[this.params,o,this.startTime,this.endTime,"fetch"],this,e.D.ajax)}function E(t){var r=this.params,n=this.metrics;if(!this.ended){this.ended=!0;for(var o=0;o 2&&void 0!==arguments[2])||arguments[2];super(e,t,we.t,r),this.importAggregator()}}new class{constructor(e){let t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:(0,_.ky)(16);c._A?(this.agentIdentifier=t,this.sharedAggregator=new y({agentIdentifier:this.agentIdentifier}),this.features={},this.desiredFeatures=new Set(e.features||[]),this.desiredFeatures.add(m),Object.assign(this,(0,a.j)(this.agentIdentifier,e,e.loaderType||"agent")),this.start()):(0,l.Z)("Failed to initial the agent. Could not determine the runtime environment.")}get config(){return{info:(0,t.C5)(this.agentIdentifier),init:(0,t.P_)(this.agentIdentifier),loader_config:(0,t.DL)(this.agentIdentifier),runtime:(0,t.OP)(this.agentIdentifier)}}start(){const t="features";try{const r=n(this.agentIdentifier),i=[...this.desiredFeatures];i.sort(((t,r)=>e.p[t.featureName]-e.p[r.featureName])),i.forEach((t=>{if(r[t.featureName]||t.featureName===e.D.pageViewEvent){const n=function(t){switch(t){case e.D.ajax:return[e.D.jserrors];case e.D.sessionTrace:return[e.D.ajax,e.D.pageViewEvent];case e.D.sessionReplay:return[e.D.sessionTrace];case e.D.pageViewTiming:return[e.D.pageViewEvent];default:return[]}}(t.featureName);n.every((e=>r[e]))||(0,l.Z)("".concat(t.featureName," is enabled but one or more dependent features has been disabled (").concat((0,D.P)(n),"). This may cause unintended consequences or missing data...")),this.features[t.featureName]=new t(this.agentIdentifier,this.sharedAggregator)}})),(0,T.Qy)(this.agentIdentifier,this.features,t)}catch(e){(0,l.Z)("Failed to initialize all enabled instrument classes (agent aborted) -",e);for(const e in this.features)this.features[e].abortHandler?.();const r=(0,T.fP)();return delete r.initializedAgents[this.agentIdentifier]?.api,delete r.initializedAgents[this.agentIdentifier]?.[t],delete this.sharedAggregator,r.ee?.abort(),delete r.ee?.get(this.agentIdentifier),!1}}}({features:[J,m,S,class extends h{static featureName=oe;constructor(t,r){if(super(t,r,oe,!(arguments.length>2&&void 0!==arguments[2])||arguments[2]),!c.il)return;const n=this.ee;let i;(0,k.QU)(n),this.eventsEE=(0,k.em)(n),this.eventsEE.on(se,(function(e,t){this.bstStart=(0,p.z)()})),this.eventsEE.on(ae,(function(t,r){(0,s.p)("bst",[t[0],r,this.bstStart,(0,p.z)()],void 0,e.D.sessionTrace,n)})),n.on(ce+ne,(function(e){this.time=(0,p.z)(),this.startPath=location.pathname+location.hash})),n.on(ce+ie,(function(t){(0,s.p)("bstHist",[location.pathname+location.hash,this.startPath,this.time],void 0,e.D.sessionTrace,n)}));try{i=new PerformanceObserver((t=>{const r=t.getEntries();(0,s.p)(te,[r],void 0,e.D.sessionTrace,n)})),i.observe({type:re,buffered:!0})}catch(e){}this.importAggregator({resourceObserver:i})}},C,xe,B,class extends h{static featureName=de;constructor(e,r){if(super(e,r,de,!(arguments.length>2&&void 0!==arguments[2])||arguments[2]),!c.il)return;if(!(0,t.OP)(e).xhrWrappable)return;try{this.removeOnAbort=new AbortController}catch(e){}let n,i=0;const o=this.ee.get("tracer"),a=(0,k._L)(this.ee),s=(0,k.Lg)(this.ee),u=(0,k.BV)(this.ee),d=(0,k.Kf)(this.ee),f=this.ee.get("events"),l=(0,k.u5)(this.ee),h=(0,k.QU)(this.ee),g=(0,k.Gm)(this.ee);function m(e,t){h.emit("newURL",[""+window.location,t])}function v(){i++,n=window.location.hash,this[ve]=(0,p.z)()}function b(){i--,window.location.hash!==n&&m(0,!0);var e=(0,p.z)();this[pe]=~~this[pe]+e-this[ve],this[ye]=e}function y(e,t){e.on(t,(function(){this[t]=(0,p.z)()}))}this.ee.on(ve,v),s.on(be,v),a.on(be,v),this.ee.on(ye,b),s.on(ge,b),a.on(ge,b),this.ee.buffer([ve,ye,"xhr-resolved"],this.featureName),f.buffer([ve],this.featureName),u.buffer(["setTimeout"+le,"clearTimeout"+fe,ve],this.featureName),d.buffer([ve,"new-xhr","send-xhr"+fe],this.featureName),l.buffer([me+fe,me+"-done",me+he+fe,me+he+le],this.featureName),h.buffer(["newURL"],this.featureName),g.buffer([ve],this.featureName),s.buffer(["propagate",be,ge,"executor-err","resolve"+fe],this.featureName),o.buffer([ve,"no-"+ve],this.featureName),a.buffer(["new-jsonp","cb-start","jsonp-error","jsonp-end"],this.featureName),y(l,me+fe),y(l,me+"-done"),y(a,"new-jsonp"),y(a,"jsonp-end"),y(a,"cb-start"),h.on("pushState-end",m),h.on("replaceState-end",m),window.addEventListener("hashchange",m,(0,O.m$)(!0,this.removeOnAbort?.signal)),window.addEventListener("load",m,(0,O.m$)(!0,this.removeOnAbort?.signal)),window.addEventListener("popstate",(function(){m(0,i>1)}),(0,O.m$)(!0,this.removeOnAbort?.signal)),this.abortHandler=this.#e,this.importAggregator()}#e(){this.removeOnAbort?.abort(),this.abortHandler=void 0}}],loaderType:"spa"})})(),window.NRBA=o})(); window.jQuery || document.write(' ') CKEDITOR_BASEPATH='https://f1000research.com/js/vendor/ckeditor/' window.reactTheme = 'research'; window.MathJax = { CommonHTML: { linebreaks: { automatic: true } }, 'HTML-CSS': { linebreaks: { automatic: true } }, SVG: { linebreaks: { automatic: true } }, AuthorInit: function() { MathJax.Hub.Register.MessageHook('End Process', function () { let timeout = false; // holder for timeout id const delay = 250; // delay after event is "complete" to run callback const reflowMath = function() { const dispFormulas = document.querySelectorAll('.disp-formula.panel'); if (!dispFormulas) { return; } for (const dispFormula of dispFormulas) { const child = dispFormula.querySelector('.MathJax_Preview').nextSibling.firstChild; const isMultiline = MathJax.Hub.getAllJax(dispFormula)[0].root.isMultiline; if (dispFormula.offsetWidth < child.offsetWidth || isMultiline) { MathJax.Hub.Queue(['Rerender', MathJax.Hub, dispFormula]); } } }; window.addEventListener('resize', function() { clearTimeout(timeout); // clear the timeout timeout = setTimeout(reflowMath, delay); // start timing for event "completion" }); }); }, }; if (window.location.hash == '#_=_'){ window.location = window.location.href.split('#')[0] } !function(f,b,e,v,n,t,s){if(f.fbq)return;n=f.fbq=function() {n.callMethod? n.callMethod.apply(n,arguments):n.queue.push(arguments)} ;if(!f._fbq)f._fbq=n; n.push=n;n.loaded=!0;n.version='2.0';n.queue=[];t=b.createElement(e);t.async=!0; t.src=v;s=b.getElementsByTagName(e)[0];s.parentNode.insertBefore(t,s)}(window, document,'script','https://connect.facebook.net/en_US/fbevents.js'); fbq('init', '1641728616063202'); fbq('track', "PixelInitialized", {}); (function(h,o,t,j,a,r){ h.hj=h.hj||function(){(h.hj.q=h.hj.q||[]).push(arguments)}; h._hjSettings={hjid:2318163,hjsv:6}; a=o.getElementsByTagName('head')[0]; r=o.createElement('script');r.async=1; r.src=t+h._hjSettings.hjid+j+h._hjSettings.hjsv; a.appendChild(r); })(window,document,'https://static.hotjar.com/c/hotjar-','.js?sv='); search file_upload Submit your research search menu close search Browse Gateways & Collections How to Publish Submit your Research My Submissions Article Guidelines Article Guidelines (New Versions) Open Data, Software and Code Guidelines Open Data and Accessible Source Materials Guidelines (HSS) Open Data, Software and Code Guidelines (PSE) Prepublication Checks Production Process Posters and Slides Guidelines Document Guidelines Article Processing Charges Peer Review Finding Article Reviewers About How it Works For Reviewers Our Advisors Policies Glossary FAQs For Developers Newsroom Contact My Research Submissions Content and Tracking Alerts My Details Sign In file_upload Submit your research { "@context": "https://schema.org", "@type": "ScholarlyArticle", "mainEntityOfPage": { "@type": "WebPage", "@id": "https://f1000research.com/articles/12-1337" }, "headline": "On solving system of differential-algebraic equations using adomian decomposition method", "datePublished": "2023-10-16T15:05:40", "dateModified": "2024-01-29T15:11:15", "author": [ { "@type": "Person", "name": "Srinivasarao Thota" }, { "@type": "Person", "name": "Shanmugasundaram P" } ], "publisher": { "@type": "Organization", "name": "F1000Research", "logo": { "@type": "ImageObject", "url": "https://f1000research.com/img/AMP/F1000Research_image.png", "height": 480, "width": 60 } }, "image": { "@type": "ImageObject", "url": "https://f1000research.com/img/AMP/F1000Research_image.png", "height": 1200, "width": 150 }, "description": " Background In this paper, we focus on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. Methods The approximate solutions are computed rapidly and efficiently with the help of a semi-analytical method known as Adomian decomposition method (ADM). The logic of this method is simple and straightforward to understand. Results To demonstrate the proposed method, we presented several examples and the computations are compared with the exact solutions to show the efficient. One can employ this logic to different mathematical software tools such as Maple, SCILab, Mathematica, NCAlgebra, Matlab etc. for the problems in real life applications. Conclusions In this paper, we offered a method for solving the given system of secondorder nonlinear DAEs with aid of the ADM. We shown that the proposed method is simple and efficient, also one can obtain the approximate solutions quickly using this method. A couple of examples are discussed for illustrating this method and graphical and mathematical assessments are discussed with the analytical solutions of the given problems. " } { "@context": "http://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": "1", "item": { "@id": "https://f1000research.com/", "name": "Home" } }, { "@type": "ListItem", "position": "2", "item": { "@id": "https://f1000research.com/browse/articles", "name": "Browse" } }, { "@type": "ListItem", "position": "3", "item": { "@id": "https://f1000research.com/articles/12-1337/v2", "name": "On solving system of differential-algebraic equations using adomian..." } } ] } Home Browse On solving system of differential-algebraic equations using adomian... ALL Metrics - Views Downloads Get PDF Get XML Cite How to cite this article Thota S and P S. On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.12688/f1000research.140257.2 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. Close Copy Citation Details Export Export Citation Sciwheel EndNote Ref. Manager Bibtex ProCite Sente EXPORT Select a format first Track Share ▬ ✚ Research Article Revised On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] Srinivasarao Thota 1 , Shanmugasundaram P https://orcid.org/0000-0002-3265-5656 2 Srinivasarao Thota 1 , Shanmugasundaram P https://orcid.org/0000-0002-3265-5656 2 PUBLISHED 29 Jan 2024 Author details Author details 1 Department of Mathematics, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh, 522503, India 2 Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Southern Nations, Nationalities, and People's Region, Ethiopia Srinivasarao Thota Roles: Conceptualization, Formal Analysis, Methodology, Resources, Software, Writing – Original Draft Preparation Shanmugasundaram P Roles: Investigation, Supervision, Validation, Writing – Review & Editing OPEN PEER REVIEW DETAILS REVIEWER STATUS Abstract Background In this paper, we focus on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. Methods The approximate solutions are computed rapidly and efficiently with the help of a semi-analytical method known as Adomian decomposition method (ADM). The logic of this method is simple and straightforward to understand. Results To demonstrate the proposed method, we presented several examples and the computations are compared with the exact solutions to show the efficient. One can employ this logic to different mathematical software tools such as Maple, SCILab, Mathematica, NCAlgebra, Matlab etc. for the problems in real life applications. Conclusions In this paper, we offered a method for solving the given system of secondorder nonlinear DAEs with aid of the ADM. We shown that the proposed method is simple and efficient, also one can obtain the approximate solutions quickly using this method. A couple of examples are discussed for illustrating this method and graphical and mathematical assessments are discussed with the analytical solutions of the given problems. READ ALL READ LESS Keywords Differential-algebraic equations, Adomian decomposition method, Approximate solutions. Corresponding Author(s) Shanmugasundaram P ( [email protected] ) Close Corresponding author: Shanmugasundaram P Competing interests: No competing interests were disclosed. Grant information: The author(s) declared that no grants were involved in supporting this work. Copyright: © 2024 Thota S and P S. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. How to cite: Thota S and P S. On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.12688/f1000research.140257.2 ) First published: 16 Oct 2023, 12 :1337 ( https://doi.org/10.12688/f1000research.140257.1 ) Latest published: 29 Jan 2024, 12 :1337 ( https://doi.org/10.12688/f1000research.140257.2 ) Revised Amendments from Version 1 Minor changes were made to the text and conclusion section. Minor changes were made to the text and conclusion section. See the authors' detailed response to the review by Mohammad Faisal Khan See the authors' detailed response to the review by Arun Prasath GM READ REVIEWER RESPONSES Introduction The applications of system of differential-algebraic equations (DAEs) occur in many branches of engineering, scientific and real life applications. For example, these equations arise in circuit analysis, electrical networks, computer aided design (CAD), optimal control, real-time simulation of mechanical (multi-body) systems, incompressible fluids dynamics, power system and chemical process simulations. DAEs are a combination of algebraic equations and differential operations, and many mathematical models in different fields are expressed in terms of DAEs. The system of DAEs is a combination of algebraic and differential equations. In the recent years, several algorithms or methods are introduced by various researchers, engineers and scientists to solve the linear/nonlinear system of DAEs and many of them are focused on the numerical solution. 7 , 13 , 14 In the literature, there are many numerical methods available and these are developed using various existing classical methods. For example, in the literature, there are numerical methods with help of Padé approximation method, 4 , 5 there are methods created using implicit Runge-Kutta methods, 36 also there are methods developed using back difference formula (BDF) 3 , 13 , 35 and etc. Many existing methods are working for low indexed problems or functions. However, using these methods, many real life applications can be solved. There are many other algorithms or methods for solving DAEs and also for differential equations available in the literature. 20 – 34 In this paper, we propose a general numerical method to solve the second-order system of DAEs using Adomian decomposition method (ADM). There are some general approaches methods available in the literature, 18 , 19 , 37 , 38 and these are developed for solving the first order DAEs. The main aim of this manuscript is to develop a method that gives us quick approximate solutions of a given system of second order DAEs. In order to develop the proposed method, we use a powerful technique, namely ADM, to get the solution of DAEs system. Since 1980, the ADM has been used widely to solve the nonlinear or linear problems in various fields. For example, recently, ADM is widely used as a straightforward powerful tool for solving a large class of nonlinear equations 1 , 2 , 8 – 12 , 15 such as functional equations, integro-differential equations (IDEs), partial differential equations (PDEs), algebraic equations, differential equations (DEs), differential-delay equations and different kind of equations arise in chemical reactions, physics and biology. We use the ADM to obtain a rapid approximation solution of a given DAEs systems. This paper is planned as follows: in the next section we recall the ADM to solve the ODEs. The method proposed in this paper for DAEs systems is presented in the following section. Then a number of numerical examples are presented to illustrate the method, followed by concluding remarks. Adomian Decomposition Method: An Overview In this section, we recall ADM briefly to solve ODEs. More details about the ADM can be found in. 2 , 9 , 15 , 17 Consider the nonlinear DE of the following type (1) Ly + Ry + N y = f , where L is an non-singular linear operator with the largest-order derivative in the DE, the operator R is the combination of the rest of derivatives in the DE, f is an analytical forcing function and N y is the nonlinear term. We can solve (1) for y by applying the inverse operator L − 1 . Indeed, we have the following solution by solving (1) for Ly and then apply the inverse operator L − 1 on to both sides, (2) L − 1 Ly = L − 1 f − L − 1 Ry − L − 1 N y or (3) y = g + L − 1 f − L − 1 Ry − L − 1 N y , where g is depending on the degree of differential operator and initial conditions. In particular, if Ly = y ′ = dy dx and the initial condition y 0 = c 0 , then L − 1 = ∫ 0 x ⋅ dx and L − 1 Ly = y − c 0 . In this case g = c 0 . If Ly = y ″ = d 2 y dx 2 and the initial condition y 0 = c 0 and y ′ 0 = c 1 , then L − 1 = ∫ 0 x ∫ 0 x ⋅ dx dx and L − 1 Ly = y − c 0 − c 1 x − 0 . In this case g = c 0 + c 1 x . To apply the ADM to (3), let y be the solution of (1), and it can be expressed in the form of infinite series as follows, (4) y = ∑ n = 0 ∞ y n , where the required components of solution y n , n = 0,1,2 , … can be computed using the ADM. The term N y can be expressed in terms of the Adomian polynomials N n , see for examples, 10 – 12 , 36 as (5) N y = ∑ n = 0 ∞ N n y 0 y 1 … y n . Now, choose y 0 as (6) y 0 = g + L − 1 f , and rewrite the equation (3) using the equations (4) and (5) , we obtain (7) ∑ n = 0 ∞ y n = y 0 − L − 1 R ∑ n = 0 ∞ y n − L − 1 ∑ n = 0 ∞ N n . On comparing the general terms of (7), we obtain the following equation for the ADM (8) y n = − L − 1 Ru n − 1 − L − 1 N n − 1 , n ≥ 1 . We have y 0 from (6), and using (8) we can generate the components y n for an approximate solution. Further, we can obtain the exact solution of (1) if the series (4) converges. The K -order approximation solution is obtained as (9) y t = ∑ n = 0 K y n . The next section presents a method for DAEs systems using the ADM. Proposed Method using ADM Consider a system of second-order DEs as follows (10) y 1 ″ = f 1 , y 2 ″ = f 2 , ⋮ y n ″ = f n , where y i ″ is the second order derivative of y i respected to the independent variable x , and f 1 , f 2 , … , f n are n unknown functions. We can rewrite the system (10), as follows: (11) Ly i = f i , i = 1 , 2 , … , n , where L = D 2 = d 2 dx 2 is the differential operator, and its inverse operator D − 1 = I = ∫ 0 x ⋅ dx . Hence L − 1 = I 2 is the secon-order inverse operator. Now we define the integral or inverse operator for the anti-derivative as follows I f x = ∫ 0 x f ξ dξ , and we have DI f = f , that is DI = 1 . The higher-order of integral operator I n is defined in the simple way, and each I n f must be continuous. In particular, I 2 f x = ∫ 0 x ∫ 0 x 1 f ξ dξ dx 1 . From replacement lemma, 16 we have the following equation. The replacement lemma helps us to convert the double integral into a single integral as given below, (12) I 2 f x = x ∫ 0 x f ξ dξ − ∫ 0 x ξf ξ dξ . Thus, (12) can be expressed in terms of integral operator I as follows I 2 f x = x I f − I xf , and in operator notation, we have I 2 = x I − I x . One can easily verify that D 2 I 2 = 1 and also D 2 x I − I x = 1 . We call x I − I x , the normal form of the integral operator I 2 . Using the inverse operator on (11), we get (13) y i = y i 0 + y i ′ 0 x + x ∫ 0 x f i dx − ∫ 0 x xf i dx , i = 1 , 2 , … , n . Applying ADM, we have the solution of (13) in the series sum, (14) y i = ∑ j = 0 ∞ f i , j , and the integrand in (13), as the sum of the following series: (15) f i = ∑ j = 0 ∞ A i , j f i , 0 f i , 1 … f i , j , where A i , j f i , 0 f i , 1 … f i , j are called Adomian polynomials. 10 – 12 , 36 Putting (14) and (15) into (13), we get (16) ∑ j = 0 ∞ f i , j = y i 0 + y i ′ 0 x + x ∫ 0 x ∑ j = 0 ∞ A i , j f i , 0 f i , 1 … f i , j dx − ∫ 0 x x ∑ j = 0 ∞ A i , j f i , 0 f i , 1 … f i , j dx , from (8) we define, for n = 0 , 1 , … , (17) f i , 0 = y i 0 + y i ′ 0 x , f i , n + 1 = x ∫ 0 x A i , n f i , 0 f i , 1 … f i , n dx − ∫ 0 x xA i , n f i , 0 f i , 1 … f i , n dx . Since f i , 0 are known, we can use f i , n + 1 to generate the approximate solution components. Numerical Examples Example 1. Let us consider the following system of second order DAEs with initial conditions to illustrate the proposed method. 39 (18) y 1 ″ − x y 2 ′ = 2 y 1 + y 2 , y 2 = e x , and initial conditions are y 1 0 = y 2 0 = y 2 ′ 0 = 1 , y 1 ′ 0 = 0 . The exact solution of this system is y 1 = 2 + 2 e 2 x + 2 − 2 e − 2 x − x + 3 e x , y 2 = e x . In order to apply the proposed method, we rewrite the given system (18) as follows y 1 ′ ′ = xy 2 ′ + 2 y 1 + y 2 , y 2 = e x . On simplifying above equations, we have y 1 ″ = 2 y 1 + x + 1 e x . Following procedure as given in (13) , we get y 1 = y 1 0 + y 1 ′ 0 x + x ∫ 0 x 2 y 1 + x + 1 e x dx − ∫ 0 x x 2 y 1 + x + 1 e x dx = 1 + x ∫ 0 x 2 y 1 + x + 1 e x dx − ∫ 0 x 2 xy 1 + x 2 + x e x dx = 1 + x ∫ 0 x x + 1 e x dx − ∫ 0 x x 2 + x e x dx + 2 x ∫ 0 x y 1 dx − 2 ∫ 0 x xy 1 dx . Use the alternate algorithm to find the Adomian polynomials as given in, 6 , 10 – 12 the Adomian method is as following: y 1 , 0 = 1 + x ∫ 0 x x + 1 e x dx − ∫ 0 x x 2 + x e x dx = 2 + xe x − e x , y 1 , n + 1 = 2 x ∫ 0 x y 1 , n dx − 2 ∫ 0 x xy 1 , n dx . We have iterations (approximate solutions components) from above equations as follows y 1 , 0 = 2 + xe x − e x , y 1 , 1 = 2 xe x + 2 x 2 − 6 e x + 4 x + 6 , y 1 , 2 = 16 x + 4 xe x + 1 3 x 4 + 4 3 x 3 + 6 x 2 + 20 − 20 e x , y 1 , 3 = 48 x + 16 3 x 3 + 8 xe x + 1 45 x 6 + 2 15 x 5 + x 4 + 20 x 2 + 56 − 56 e x . Now we have the approximate solution after three steps y apx 3 = ∑ j = 0 3 f 1 , j = 84 + 15 xe x − 83 e x + 28 x 2 + 68 x + 4 3 x 4 + 20 3 x 3 + 1 45 x 6 + 1 15 x 5 . After nine steps, we have the solution y apx 9 = 17412 + 16388 x + 1023 xe x − 17411 e x + 7684 x 2 + 17 24324300 x 13 + 1 89100 x 12 + 1 347351004000 x 17 + 1 10216206000 x 16 + 7 44550 x 11 + 19 9450 x 10 + 43 1890 x 9 + 29 126 x 8 + 1 510810300 x 15 + 214 105 x 7 + 706 45 x 6 + 1538 15 x 5 + 1666 3 x 4 + 1 6252318072000 x 18 + 7172 3 x 3 + 1 24324300 x 14 . Graphical assessment of the analytic solution with the approximate solution after three steps is visualized in Figure 1 and the comparison of the exact solution with approximate solution after nine steps is shown in Figure 2 . From these figures, we can observe that the approximate solutions are near to the analytic solution. A greater number of steps gives us a more accurate solution (the graphs are drawn using Maple 16.0). Figure 1. Assessment of y apx 3 with Exact solution y 1 . Figure 2. Assessment of y apx 9 with Exact solution y 1 . Numerical results of the exact solution, approximate solution y apx 3 after three steps, approximate solution y apx 9 after nine steps and absolute error are given in Table 1 . From the numerical values in Table 1 , one can observe that the solution y apx 9 is closer to the exact solution y 1 . To get more appropriate solution of the given system, we increase the number of iterations. Table 1. Mathematical results for Example 1. x y 1 x y apx 3 x y apx 9 x | y 1 x − y apx 9 x | − 2.0 9.977284737 9.862668553 9.977273565 1.117 × 10 − 5 − 1.0 2.503779856 2.503370315 2.503780041 1.850 × 10 − 7 − 0.5 1.355157416 1.355155845 1.3551542 3.216 × 10 − 6 0.5 1.442726178 1.442724586 1.4427204 5.778 × 10 − 6 1.0 3.31280240 3.312391255 3.312807041 4.641 × 10 − 5 1.5 8.38448291 8.373436300 8.384502002 1.909 × 10 − 5 2.0 20.85383714 20.73558235 20.85388357 4.643 × 10 − 5 2.5 50.16639112 49.39270508 50.16642510 3.398 × 10 − 5 3.0 117.0950239 113.3495974 117.0950934 6.950 × 10 − 5 3.5 266.6334832 251.7748955 266.6334147 6.850 × 10 − 5 4.0 595.1225779 543.7981055 595.1220909 4.870 × 10 − 4 Example 2. Consider a DAEs system of second order. 39 (19) y 1 ″ − 2 xy 3 ′ − y 1 − 2 y 2 = 0 , y 2 ″ + y 2 − 2 y 3 = 2 e x , y 3 = cos x , with initial conditions y 1 0 = 0 , y 1 ′ 0 = y 2 0 = y 2 ′ 0 = 1 . The analytical solution of this system is y 1 = xe x , y 2 = e x + x sin x , y 3 = cos x . After simplifying the system (19) , we get y 1 ″ = y 1 + 2 y 2 − 2 x sin x , y 2 ″ = − y 2 + 2 e x + 2 cos x , y 3 = cos x . Following the procedure of the proposed method, similar to Example 1 , we get y 1 = y 1 0 + y 1 ′ 0 x + x ∫ 0 x y 1 + 2 y 2 − 2 x sin x dx − ∫ 0 x x y 1 + 2 y 2 − 2 x sin x dx = x − 2 x ∫ 0 x x sin x dx + 2 ∫ 0 x x sin x dx + x ∫ 0 x y 1 + 2 y 2 dx − ∫ 0 x y 1 + 2 y 2 dx , y 2 = y 2 0 + y 2 ′ 0 x + x ∫ 0 x − y 2 + 2 e x + 2 cos x dx − ∫ 0 x x − y 2 + 2 e x + 2 cos x dx = 1 + x + 2 x ∫ 0 x e x + cos x dx − 2 ∫ 0 x x e x + cos x dx − x ∫ 0 x y 2 dx + ∫ 0 x y 2 dx . Using the alternate algorithm for computing the Adomian polynomials, we have y 1 , 0 = x − x ∫ 0 x 2 x sin x dx + ∫ 0 x 2 x 2 sin x dx = x − 4 + 4 cos x + 2 x sin x , y 2 , 0 = 1 + x + 2 x ∫ 0 x e x + cos x dx − 2 ∫ 0 x x e x + cos x dx = 1 − x + 2 e x − 2 cos x , y 1 , n + 1 = x ∫ 0 x y 1 , n + y 2 , n dx − ∫ 0 x y 1 , n + y 2 , n dx , y 2 , n + 1 = − x ∫ 0 x y 2 , n dx + ∫ 0 x y 2 , n dx . Now, we can get iterations from above equations as follows y 1 , 0 = x − 4 + 4 cos x + 2 x sin x , y 2 , 0 = 1 − x + 2 e x − 2 cos x , y 1 , 1 = − 4 x − 1 5 x 3 − x 2 − 4 cos x − 2 x sin x + 4 e x , y 2 , 1 = 4 + 2 x − 1 2 x 2 + 1 6 x 3 − 2 e x − 2 cos x , y 1 , 2 = − 12 + 1 120 x 5 − 1 6 x 4 + 12 cos x + 2 x sin x + 4 x 2 , y 2 , 2 = − 2 x − 2 x 2 − 1 3 x 3 + 1 24 x 4 − 1 120 x 5 + 2 e x − 2 cos x , ⋮ After five steps, we have the solution y 1 , apx 5 = − 12 − 11 x + 12 e x − 1 1008 x 7 − 1 10080 x 8 − 1 120 x 6 − 7 120 x 5 − 1 3 x 4 − 5 x 2 − 1 120960 x 9 − 3 2 x 3 − 1 39916800 x 11 − 1 1814400 x 10 , y 2 , apx 5 = 13 + x − 12 cos x + 1 5040 x 7 + 1 8064 x 8 − 1 144 x 6 + 1 120 x 5 + 3 8 x 4 − 9 2 x 2 + 1 362880 x 9 + 1 6 x 3 + 1 39916800 x 11 − 1 3628800 x 10 . In Figure 3 and Figure 4 , we show the graphical comparisons of the exact solutions y 1 x , y 2 x with the approximate solution after five steps respectively. From the graphs in Figure 3 and Figure 4 , one can observe that the approximate solutions are very close to the exact solution. Higher number of iterations give us more accurate solution (one can use Microsoft Excel to draw the graphs). Figure 3. Assessment of y 1 , apx 5 with Exact solution y 1 . Figure 4. Assessment of y 2 , apx 5 with Exact solution y 2 . In Table 2 and Table 3 , mathematical results of the analytical solution and approximate solutions after five steps y 1 , apx 5 , y 2 , apx 5 with absolute errors are given respectively. From these numerical results, one can observe that the approximate solutions y 1 , apx 5 and y 2 , apx 5 are closer to the exact solution y 1 and y 2 respectively. For more appropriate solution of the given system, we increase the number of iterations. Table 2. Mathematical results for Example 2. x Exact value y 1 x y 1 , apx 5 x | y 1 x − y 1 , apx 5 x | 0.1 0.1105170918 0.1105170950 3.2 × 10 − 9 0.2 0.2442805516 0.2442805537 2.1 × 10 − 9 0.4 0.5967298792 0.5967298887 9.5 × 10 − 9 0.6 1.093271280 1.093271277 3.0 × 10 − 9 0.8 1.780432742 1.780432741 1.0 × 10 − 9 1.0 2.718281828 2.718281829 1.0 × 10 − 9 Table 3. Mathematical results for Example 2. x Exact value y 2 x y 2 , apx 5 x | y 2 x − y 2 , apx 5 x | 0.1 1.115154260 1.115154263 3.0 × 10 − 9 0.2 1.261136624 1.261136629 5.0 × 10 − 9 0.4 1.647592035 1.647592033 2.0 × 10 − 9 0.6 2.160904284 2.160904284 0 0.8 2.799425801 2.799425801 0 1.0 3.559752813 3.559752811 2.0 × 10 − 9 Conclusions In this paper, we offered/presented a numerical method for solving the given system of second-order nonlinear DAEs with aid of the ADM. We illustrated and shown that the proposed method is simple and efficient, also one can obtain the approximate solutions quickly using this method. Logic of the method in this paper is straightforward and simple. Data availability Underlying data Mendeley data: On solving system of DAEs using ADM https://doi.org/10.17632/r89zy3y657.1 . 39 This project contains the following underlying data: • Paper_Example_1.mw • Paper_Example_2.mw Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0). Acknowledgement The author is thankful to the reviewers and editor for providing valuable inputs to improve the quality and present format of this manuscript. References 1. Wazwaz AM: A new approach to the nonlinear advection problem: An application of the decomposition technique. Appl. Math. Comput. 1995; 72 : 175–181. Publisher Full Text 2. Benhammouda B: A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method. Springerplus. 2016; 5 : 590. PubMed Abstract | Publisher Full Text | Free Full Text 3. Gear CW, Petzold LR: ODE systems for the solution of differential algebraic systems. SIAM J. Numer. Anal. 1984; 21 : 716–728. Publisher Full Text 4. Çelik E, Karaduman E, Bayram M: Numerical Method to Solve Chemical Differential-Algebraic Equations. Int. J. Quantum Chem. 2002; 89 : 447–451. Publisher Full Text 5. Çelik E, Bayram M: On the numerical solution of differential-algebraic equations by Padé series. Appl. Math. Comput. 2003; 137 : 151–160. Publisher Full Text 6. Çelik E, Bayram M, Yeloğlu T: Solution of Differential-Algebraic Equations (DAEs) by Adomian Decomposition Method. International Journal Pure & Applied Mathematical Sciences. 2006; 3 (1): 93–100. 7. Hairer E, Norsett SP, Wanner G: Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. New York: Springer; 1992. 978-3-642-05221-7. 8. Aomian G: Nonlinear Stochastic Systems Theory and Applications to Physics. Dordrecht/Norwell, MA: Kluwer Acaemic; 1989. 9. Adomian G, Rach R: On the solution of algebraic equations by the decomposition method. J. Math. Anal. Appl. 1985; 105 (1): 141–166. Publisher Full Text 10. Duan JS: Recurrence triangle for Adomian polynomials. Appl. Math. Comput. 2010; 216 : 1235–1241. Publisher Full Text 11. Duan JS: An efficient algorithm for the multivariable Adomian polynomials. Appl. Math. Comput. 2010; 217 : 2456–2467. Publisher Full Text 12. Duan JS: Convenient analytic recurrence algorithms for the Adomian polynomials. Appl. Math. Comput. 2011; 217 : 6337–6348. Publisher Full Text 13. Brenan KE, Campbell SL, Petzold LR: Numerical Solution of Initial Value Problems in Differential-Algebraic Equations. SIAM Philadelphia. 1989; 26 : 976–996. 978-0-89871-353-4. Publisher Full Text 14. Petzold LR: Numerical Solution of Differential-Algebraic Equations. Advances in Numerical Analysis IV. 1995. 15. Almazmumy M, Hendi FA, Bakodah HO, et al. : Recent modifications of Adomian decomposition method for initial value problem in ordinary differential equations. Am. J. Comput. Math. 2012; 02 : 228–234. Publisher Full Text 16. Peter J: Collins: Differential and integral equations. Oxford University Press; 2006. 17. Ramana PV, Raghu Prasad BK: Modified Adomian decomposition method for Van der Pol equations. Int. J. Non Linear Mech. 2014; 65 : 121–132. Publisher Full Text 18. Campbell SL: A Computational method for general higher index singular systems of differential equations. IMACS Trans. Sci. Comput. 1989; 89 : 555–560. 19. Campbell SL, Moore E, Zhong Y: Utilization of automatic differentiation in control algorithms. IEEE Trans. Automat. Control. 1994; 39 : 1047–1052. Publisher Full Text 20. Thota S, Kumar SD: Solving system of higher-order linear differential equations on the level of operators. International journal of pure and applied mathematics. 2016; 106 (1): 11–21. Publisher Full Text 21. Thota S, Kumar SD: On a mixed interpolation with integral conditions at arbitrary nodes. Cogent Mathematics. 2016; 3 (1): 1–10. Publisher Full Text 22. Thota S, Kumar SD: Symbolic algorithm for a system of differential-algebraic equations. Kyungpook Mathematical Journal. 2016; 56 (4): 1141–1160. Publisher Full Text 23. Thota S, Kumar SD: A new method for general solution of system of higher-order linear differential equations. International Conference on Inter Disciplinary Research in Engineering and Technology. 2015; 1 : 240–243. 24. Thota S, Kumar SD: Symbolic method for polynomial interpolation with Stieltjes conditions. International Conference on Frontiers in Mathematics. 2015; 225–228. 25. Thota S, Rosenkranz M, Kumar SD: Solving systems of linear differential equations over integro-differential algebras. International Conference on Applications of Computer Algebra, June 24–29, 2012, Sofia, Bulgaria. 26. Thota S: A Study on Symbolic Algorithms for Solving Ordinary and Partial Linear Differential Equations, Ph.D. thesis.2017. 27. Thota S, Kumar SD: Maple Implementation of Symbolic Methods for Initial Value Problems. Research for Resurgence-An Edited Multidisciplinary Research Book. 2017; I : 240–243. 28. Thota S: On a Symbolic Method for Fully Inhomogeneous Boundary Value Problems. Kyungpook Mathematical Journal. 2019; 59 (1): 13–22. 29. Thota S: On A New Symbolic Method for Initial Value Problems for Systems of Higher-order Linear Differential Equations, International Journal of. Mathematical Models and Methods in Applied Sciences. 2018; 12 : 194–202. 30. Thota S: A Symbolic Algorithm for Polynomial Interpolation with Integral Conditions. Applied Mathematics & Information Sciences. 2018; 12 (5): 995–1001. Publisher Full Text 31. Thota S: Initial value problems for system of differential-algebraic equations in Maple. BMC. Res. Notes. 2018; 11 : 651. PubMed Abstract | Publisher Full Text | Free Full Text 32. Thota S: On A Symbolic Method for Error Estimation of a Mixed Interpolation. Kyungpook Mathematical Journal. 2018; 58 (3): 453–462. 33. Thota S: A Symbolic Algorithm for Polynomial Interpolation with Stieltjes Conditions in Maple. Proceedings of the Institute of Applied mathematics. 2019; 8 (2): 112–120. 34. Thota S: On A New Symbolic Method for Solving Two-point Boundary Value Problems with Variable Coefficients, International Journal of. Math. Comput. Simul. 2019; 13 : 160–164. 35. Ascher UM: On symmetric schemes and differential-algebraic equations. SIAM J. Sci. Stat. Comput. 1989; 10 : 937–949. Publisher Full Text 36. Ascher UM, Petzold LR: Projected implicit Runge Kutta methods for differential-algebraic equations. SIAM J. Numer. Anal. 1991; 28 : 1097–1120. Publisher Full Text 37. Ascher UM, Lin P: Sequential regularization methods for higher index differential-algebraic equations with constant singularities: the linear index-2 case. SIAM J. Numer. Anal. 1996; 33 : 1921–1940. Publisher Full Text 38. Ascher UM, Lin P: Sequential regularization methods for non-linear higher index differential-algebraic equations. SIAM J. Sci. Comput. 1997; 18 : 160–181. Publisher Full Text 39. Palanisamy S, Thota S: On solving system of DAEs using ADM. [Data]. Mendeley Data. 2023; V1 . Publisher Full Text Comments on this article Comments (1) Version 2 VERSION 2 PUBLISHED 29 Jan 2024 Revised Comment ADD YOUR COMMENT Version 1 VERSION 1 PUBLISHED 16 Oct 2023 Discussion is closed on this version, please comment on the latest version above. Reader Comment 06 Nov 2023 Brahim Benhammouda , Higher Colleges of Technology, United Arab Emirates 06 Nov 2023 Reader Comment The paper discusses a semi-analytical solution of DAEs using the Adomian decomposition method. All the numerical examples solved consist of ODEs coupled with an algebraic equation that gives the ... Continue reading The paper discusses a semi-analytical solution of DAEs using the Adomian decomposition method. All the numerical examples solved consist of ODEs coupled with an algebraic equation that gives the algebraic variable explicitly. This type of equations are simple index-1 DAEs where the algebraic variable is given explicitly as a function of the independent variable x. Such equations present no difficulty at all. I think the paper will be of interest in it discusses nonlinear index-1 and higher indices like for example the pendulum problem. The paper discusses a semi-analytical solution of DAEs using the Adomian decomposition method. All the numerical examples solved consist of ODEs coupled with an algebraic equation that gives the algebraic variable explicitly. This type of equations are simple index-1 DAEs where the algebraic variable is given explicitly as a function of the independent variable x. Such equations present no difficulty at all. I think the paper will be of interest in it discusses nonlinear index-1 and higher indices like for example the pendulum problem. Competing Interests: No competing interests were disclosed. Close Report a concern Discussion is closed on this version, please comment on the latest version above. Author details Author details 1 Department of Mathematics, Amrita Vishwa Vidyapeetham, Amaravati, Andhra Pradesh, 522503, India 2 Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Southern Nations, Nationalities, and People's Region, Ethiopia Srinivasarao Thota Roles: Conceptualization, Formal Analysis, Methodology, Resources, Software, Writing – Original Draft Preparation Shanmugasundaram P Roles: Investigation, Supervision, Validation, Writing – Review & Editing Competing interests No competing interests were disclosed. Grant information The author(s) declared that no grants were involved in supporting this work. Article Versions (2) version 2 Revised Published: 29 Jan 2024, 12:1337 https://doi.org/10.12688/f1000research.140257.2 version 1 Published: 16 Oct 2023, 12:1337 https://doi.org/10.12688/f1000research.140257.1 Copyright © 2024 Thota S and P S. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Download Export To Sciwheel Bibtex EndNote ProCite Ref. Manager (RIS) Sente metrics Views Downloads F1000Research - - PubMed Central info_outline Data from PMC are received and updated monthly. - - Citations open_in_new 0 open_in_new 0 open_in_new SEE MORE DETAILS CITE how to cite this article Thota S and P S. On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.12688/f1000research.140257.2 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS track receive updates on this article Track an article to receive email alerts on any updates to this article. TRACK THIS ARTICLE Share Open Peer Review Current Reviewer Status: ? Key to Reviewer Statuses VIEW HIDE Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Version 2 VERSION 2 PUBLISHED 29 Jan 2024 Revised Views 0 Cite How to cite this report: Prasath GM A. Reviewer Report For: On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.5256/f1000research.161819.r243839 ) The direct URL for this report is: https://f1000research.com/articles/12-1337/v2#referee-response-243839 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 14 May 2024 Arun Prasath GM , Department of Information Technology, University of Technology and Applied Sciences, Muscat, Oman Approved VIEWS 0 https://doi.org/10.5256/f1000research.161819.r243839 This paper focused on an efficient and easy method to solve the second-order systems of differential-algebraic equations (DAEs). They computed the approximate solutions with the help of a semi-analytical method known as “Adomian decomposition method” (ADM). They claimed that the ... Continue reading READ ALL This paper focused on an efficient and easy method to solve the second-order systems of differential-algebraic equations (DAEs). They computed the approximate solutions with the help of a semi-analytical method known as “Adomian decomposition method” (ADM). They claimed that the logic of the proposed method is simple and straightforward to understand. Authors presented few examples to illustrate the method. The paper is attractive and planned fine. The key of this paper is to solve the given system of DAEs with the help of ADM to give speedy approximate solution. The design of the work in this paper is constructive and novel. I recommend, this paper can be acceptable. After review, the authors can include the following comments. Comments: This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Integral operator is fixed with lower-limit as zero or it can be any constant? Give explanation about it. Is the work clearly and accurately presented and does it cite the current literature? Yes Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests: No competing interests were disclosed. Reviewer Expertise: Inventory Model, Parking lot problems, Analytic Hierarchy Process, Optimization I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Prasath GM A. Reviewer Report For: On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.5256/f1000research.161819.r243839 ) The direct URL for this report is: https://f1000research.com/articles/12-1337/v2#referee-response-243839 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 29 Jun 2024 Shanmugasundaram P , Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Ethiopia 29 Jun 2024 Author Response * This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Response: The proposed ... Continue reading * This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. This information is given conclusion section. * Integral operator is fixed with lower-limit as zero or it can be any constant? Give explanation about it. Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. There is no restriction on lower bound of the integral. * This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. This information is given conclusion section. * Integral operator is fixed with lower-limit as zero or it can be any constant? Give explanation about it. Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. There is no restriction on lower bound of the integral. Competing Interests: No. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 29 Jun 2024 Shanmugasundaram P , Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Ethiopia 29 Jun 2024 Author Response * This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Response: The proposed ... Continue reading * This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. This information is given conclusion section. * Integral operator is fixed with lower-limit as zero or it can be any constant? Give explanation about it. Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. There is no restriction on lower bound of the integral. * This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. This information is given conclusion section. * Integral operator is fixed with lower-limit as zero or it can be any constant? Give explanation about it. Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. There is no restriction on lower bound of the integral. Competing Interests: No. Close Report a concern COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Faisal Khan M. Reviewer Report For: On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.5256/f1000research.161819.r243837 ) The direct URL for this report is: https://f1000research.com/articles/12-1337/v2#referee-response-243837 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 05 Mar 2024 Mohammad Faisal Khan , Saudi Electronic University, Riyadh, Riyadh Province, Saudi Arabia Approved VIEWS 0 https://doi.org/10.5256/f1000research.161819.r243837 Authors focused on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. The method includes computing the approximate solutions with rapidly and efficiently with the help of a semi-analytical method known as ... Continue reading READ ALL Authors focused on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. The method includes computing the approximate solutions with rapidly and efficiently with the help of a semi-analytical method known as Adomian decomposition method (ADM). The logic of this method is simple and straightforward to understand. To demonstrate the proposed method, they presented several examples and the computations are compared with the exact solutions to show the efficient. They also claimed that one can employ this logic to different mathematical software tools such as Maple, SCILab, Mathematica, NCAlgebra, Matlab etc. for the problems in real life applications. General Comments: The paper is organized in well-order and interesting to the general readers. The main text is to propose a method for DAEs using ADM which produces quick approximate solution which is novel as far as my knowledge. This paper can be accepted . Minor comments: In the paper, authors are focused on only second order DAEs. Is this technique applicable for higher order DAEs? In the integral operator I, authors have taken lower value of the integral zero. What is the reason for fixed lower value zero? If the lower value is not fixed, say c (constant), that are changes occur in the process? Is the work clearly and accurately presented and does it cite the current literature? Yes Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Yes Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests: No competing interests were disclosed. Reviewer Expertise: Optimisation, Special functions, I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Faisal Khan M. Reviewer Report For: On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.5256/f1000research.161819.r243837 ) The direct URL for this report is: https://f1000research.com/articles/12-1337/v2#referee-response-243837 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 13 Apr 2024 Shanmugasundaram P , Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Ethiopia 13 Apr 2024 Author Response The authors of this paper are very thankful to the reviewer for giving valuable comments on this paper. The response to the minor comments are as follows: 1. In ... Continue reading The authors of this paper are very thankful to the reviewer for giving valuable comments on this paper. The response to the minor comments are as follows: 1. In the paper, authors are focused on only second order DAEs. Is this technique applicable for higher order DAEs? Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. 2. In the integral operator I, authors have taken lower value of the integral zero. What is the reason for a fixed lower value of zero? If the lower value is not fixed, say c (constant), are changes occur in the process? Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. The authors of this paper are very thankful to the reviewer for giving valuable comments on this paper. The response to the minor comments are as follows: 1. In the paper, authors are focused on only second order DAEs. Is this technique applicable for higher order DAEs? Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. 2. In the integral operator I, authors have taken lower value of the integral zero. What is the reason for a fixed lower value of zero? If the lower value is not fixed, say c (constant), are changes occur in the process? Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. Competing Interests: No. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 13 Apr 2024 Shanmugasundaram P , Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Ethiopia 13 Apr 2024 Author Response The authors of this paper are very thankful to the reviewer for giving valuable comments on this paper. The response to the minor comments are as follows: 1. In ... Continue reading The authors of this paper are very thankful to the reviewer for giving valuable comments on this paper. The response to the minor comments are as follows: 1. In the paper, authors are focused on only second order DAEs. Is this technique applicable for higher order DAEs? Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. 2. In the integral operator I, authors have taken lower value of the integral zero. What is the reason for a fixed lower value of zero? If the lower value is not fixed, say c (constant), are changes occur in the process? Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. The authors of this paper are very thankful to the reviewer for giving valuable comments on this paper. The response to the minor comments are as follows: 1. In the paper, authors are focused on only second order DAEs. Is this technique applicable for higher order DAEs? Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. 2. In the integral operator I, authors have taken lower value of the integral zero. What is the reason for a fixed lower value of zero? If the lower value is not fixed, say c (constant), are changes occur in the process? Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. Competing Interests: No. Close Report a concern COMMENT ON THIS REPORT Comments on this article Comments (1) Version 2 VERSION 2 PUBLISHED 29 Jan 2024 Revised Comment ADD YOUR COMMENT Version 1 VERSION 1 PUBLISHED 16 Oct 2023 Discussion is closed on this version, please comment on the latest version above. Reader Comment 06 Nov 2023 Brahim Benhammouda , Higher Colleges of Technology, United Arab Emirates 06 Nov 2023 Reader Comment The paper discusses a semi-analytical solution of DAEs using the Adomian decomposition method. All the numerical examples solved consist of ODEs coupled with an algebraic equation that gives the ... Continue reading The paper discusses a semi-analytical solution of DAEs using the Adomian decomposition method. All the numerical examples solved consist of ODEs coupled with an algebraic equation that gives the algebraic variable explicitly. This type of equations are simple index-1 DAEs where the algebraic variable is given explicitly as a function of the independent variable x. Such equations present no difficulty at all. I think the paper will be of interest in it discusses nonlinear index-1 and higher indices like for example the pendulum problem. The paper discusses a semi-analytical solution of DAEs using the Adomian decomposition method. All the numerical examples solved consist of ODEs coupled with an algebraic equation that gives the algebraic variable explicitly. This type of equations are simple index-1 DAEs where the algebraic variable is given explicitly as a function of the independent variable x. Such equations present no difficulty at all. I think the paper will be of interest in it discusses nonlinear index-1 and higher indices like for example the pendulum problem. Competing Interests: No competing interests were disclosed. Close Report a concern Discussion is closed on this version, please comment on the latest version above. keyboard_arrow_left keyboard_arrow_right Open Peer Review Reviewer Status info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Reviewer Reports Invited Reviewers 1 2 Version 2 (revision) 29 Jan 24 read read Version 1 16 Oct 23 Mohammad Faisal Khan , Saudi Electronic University, Riyadh, Saudi Arabia Arun Prasath GM , University of Technology and Applied Sciences, Muscat, Oman Comments on this article All Comments (1) Add a comment Sign up for content alerts Sign Up You are now signed up to receive this alert Browse by related subjects keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2024 Prasath GM A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 14 May 2024 | for Version 2 Arun Prasath GM , Department of Information Technology, University of Technology and Applied Sciences, Muscat, Oman 0 Views copyright © 2024 Prasath GM A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions This paper focused on an efficient and easy method to solve the second-order systems of differential-algebraic equations (DAEs). They computed the approximate solutions with the help of a semi-analytical method known as “Adomian decomposition method” (ADM). They claimed that the logic of the proposed method is simple and straightforward to understand. Authors presented few examples to illustrate the method. The paper is attractive and planned fine. The key of this paper is to solve the given system of DAEs with the help of ADM to give speedy approximate solution. The design of the work in this paper is constructive and novel. I recommend, this paper can be acceptable. After review, the authors can include the following comments. Comments: This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Integral operator is fixed with lower-limit as zero or it can be any constant? Give explanation about it. Is the work clearly and accurately presented and does it cite the current literature? Yes Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests No competing interests were disclosed. Reviewer Expertise Inventory Model, Parking lot problems, Analytic Hierarchy Process, Optimization I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. reply Respond to this report Responses (1) Author Response 29 Jun 2024 Shanmugasundaram P, Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Ethiopia * This paper solves second order DAEs. Can we apply the same logic for higher order DAEs, if so; put it as NOTE point in the conclusion section. Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. This information is given conclusion section. * Integral operator is fixed with lower-limit as zero or it can be any constant? Give explanation about it. Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. There is no restriction on lower bound of the integral. View more View less Competing Interests No. reply Respond Report a concern Prasath GM A. Peer Review Report For: On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.5256/f1000research.161819.r243839) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/12-1337/v2#referee-response-243839 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2024 Faisal Khan M. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 05 Mar 2024 | for Version 2 Mohammad Faisal Khan , Saudi Electronic University, Riyadh, Riyadh Province, Saudi Arabia 0 Views copyright © 2024 Faisal Khan M. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Authors focused on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. The method includes computing the approximate solutions with rapidly and efficiently with the help of a semi-analytical method known as Adomian decomposition method (ADM). The logic of this method is simple and straightforward to understand. To demonstrate the proposed method, they presented several examples and the computations are compared with the exact solutions to show the efficient. They also claimed that one can employ this logic to different mathematical software tools such as Maple, SCILab, Mathematica, NCAlgebra, Matlab etc. for the problems in real life applications. General Comments: The paper is organized in well-order and interesting to the general readers. The main text is to propose a method for DAEs using ADM which produces quick approximate solution which is novel as far as my knowledge. This paper can be accepted . Minor comments: In the paper, authors are focused on only second order DAEs. Is this technique applicable for higher order DAEs? In the integral operator I, authors have taken lower value of the integral zero. What is the reason for fixed lower value zero? If the lower value is not fixed, say c (constant), that are changes occur in the process? Is the work clearly and accurately presented and does it cite the current literature? Yes Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Yes Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests No competing interests were disclosed. Reviewer Expertise Optimisation, Special functions, I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. reply Respond to this report Responses (1) Author Response 13 Apr 2024 Shanmugasundaram P, Department of Mathematics, Mizan-Tepi University, Mizan Teferi, Ethiopia The authors of this paper are very thankful to the reviewer for giving valuable comments on this paper. The response to the minor comments are as follows: 1. In the paper, authors are focused on only second order DAEs. Is this technique applicable for higher order DAEs? Response: The proposed technique in this paper is applicable to the higher-order DAEs. For the sake of simplicity, we have taken 2-order DAEs. 2. In the integral operator I, authors have taken lower value of the integral zero. What is the reason for a fixed lower value of zero? If the lower value is not fixed, say c (constant), are changes occur in the process? Response: The lower value of the integral can be any number. Based on this, we compute integrals in the proposed algorithm. For simplicity, we took the lower value to be zero. View more View less Competing Interests No. reply Respond Report a concern Faisal Khan M. Peer Review Report For: On solving system of differential-algebraic equations using adomian decomposition method [version 2; peer review: 2 approved] . F1000Research 2024, 12 :1337 ( https://doi.org/10.5256/f1000research.161819.r243837) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/12-1337/v2#referee-response-243837 Alongside their report, reviewers assign a status to the article: Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions Adjust parameters to alter display View on desktop for interactive features Includes Interactive Elements View on desktop for interactive features Competing Interests Policy Provide sufficient details of any financial or non-financial competing interests to enable users to assess whether your comments might lead a reasonable person to question your impartiality. Consider the following examples, but note that this is not an exhaustive list: Examples of 'Non-Financial Competing Interests' Within the past 4 years, you have held joint grants, published or collaborated with any of the authors of the selected paper. You have a close personal relationship (e.g. parent, spouse, sibling, or domestic partner) with any of the authors. You are a close professional associate of any of the authors (e.g. scientific mentor, recent student). You work at the same institute as any of the authors. You hope/expect to benefit (e.g. favour or employment) as a result of your submission. You are an Editor for the journal in which the article is published. Examples of 'Financial Competing Interests' You expect to receive, or in the past 4 years have received, any of the following from any commercial organisation that may gain financially from your submission: a salary, fees, funding, reimbursements. You expect to receive, or in the past 4 years have received, shared grant support or other funding with any of the authors. You hold, or are currently applying for, any patents or significant stocks/shares relating to the subject matter of the paper you are commenting on. Stay Updated Sign up for content alerts and receive a weekly or monthly email with all newly published articles Register with F1000Research Already registered? Sign in Not now, thanks close PLEASE NOTE If you are an AUTHOR of this article, please check that you signed in with the account associated with this article otherwise we cannot automatically identify your role as an author and your comment will be labelled as a “User Comment”. If you are a REVIEWER of this article, please check that you have signed in with the account associated with this article and then go to your account to submit your report, please do not post your review here. If you do not have access to your original account, please contact us . All commenters must hold a formal affiliation as per our Policies . The information that you give us will be displayed next to your comment. User comments must be in English, comprehensible and relevant to the article under discussion. We reserve the right to remove any comments that we consider to be inappropriate, offensive or otherwise in breach of the User Comment Terms and Conditions . Commenters must not use a comment for personal attacks. When criticisms of the article are based on unpublished data, the data should be made available. I accept the User Comment Terms and Conditions Please confirm that you accept the User Comment Terms and Conditions. Affiliation ✕ refresh Please enter your institution. Note: To add your institution or organisation, start typing the name and then select the correct name from the list. Where applicable, the name will appear in both the original language and in English. Do not paste in the name. If the name does not appear in the drop-down list, we will display the information you have entered. ✕ refresh Country/Region * USA UK Canada China France Germany Afghanistan Aland Islands Albania Algeria American Samoa Andorra Angola Anguilla Antarctica Antigua and Barbuda Argentina Armenia Aruba Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bermuda Bhutan Bolivia Bosnia and Herzegovina Botswana Bouvet Island Brazil British Indian Ocean Territory British Virgin Islands Brunei Bulgaria Burkina Faso Burundi Cambodia Cameroon Canada Cape Verde Cayman Islands Central African Republic Chad Chile China Christmas Island Cocos (Keeling) Islands Colombia Comoros Congo Cook Islands Costa Rica Cote d'Ivoire Croatia Cuba Cyprus Czech Republic Democratic Republic of the Congo Denmark Djibouti Dominica Dominican Republic Ecuador Egypt El Salvador Equatorial Guinea Eritrea Estonia Ethiopia Falkland Islands Faroe Islands Federated States of Micronesia Fiji Finland France French Guiana French Polynesia French Southern Territories Gabon Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guadeloupe Guam Guatemala Guernsey Guinea Guinea-Bissau Guyana Haiti Heard Island and Mcdonald Islands Holy See (Vatican City State) Honduras Hong Kong Hungary Iceland India Indonesia Iran Iraq Ireland Israel Italy Jamaica Japan Jersey Jordan Kazakhstan Kenya Kiribati Kosovo (Serbia and Montenegro) Kuwait Kyrgyzstan Lao People's Democratic Republic Latvia Lebanon Lesotho Liberia Libya Liechtenstein Lithuania Luxembourg Macao Madagascar Malawi Malaysia Maldives Mali Malta Marshall Islands Martinique Mauritania Mauritius Mayotte Mexico Minor Outlying Islands of the United States Moldova Monaco Mongolia Montenegro Montserrat Morocco Mozambique Myanmar Namibia Nauru Nepal Netherlands Antilles New Caledonia New Zealand Nicaragua Niger Nigeria Niue Norfolk Island North Korea North Macedonia Northern Mariana Islands Norway Oman Pakistan Palau Palestinian Territory Panama Papua New Guinea Paraguay Peru Philippines Pitcairn Poland Portugal Puerto Rico Qatar Reunion Romania Russian Federation Rwanda Saint Helena Saint Kitts and Nevis Saint Lucia Saint Pierre and Miquelon Saint Vincent and the Grenadines Samoa San Marino Sao Tome and Principe Saudi Arabia Senegal Serbia Seychelles Sierra Leone Singapore Slovakia Slovenia Solomon Islands Somalia South Africa South Georgia and the South Sandwich Is South Korea South Sudan Spain Sri Lanka Sudan Suriname Svalbard and Jan Mayen Swaziland Sweden Switzerland Syria Taiwan Tajikistan Tanzania Thailand The Gambia The Netherlands Timor-Leste Togo Tokelau Tonga Trinidad and Tobago Tunisia Turkey Turkmenistan Turks and Caicos Islands Tuvalu UK USA Uganda Ukraine United Arab Emirates United States Virgin Islands Uruguay Uzbekistan Vanuatu Venezuela Vietnam Wallis and Futuna West Bank and Gaza Strip Western Sahara Yemen Zambia Zimbabwe Please select your country/region. You must enter a comment. Competing Interests Please disclose any competing interests that might be construed to influence your judgment of the article's or peer review report's validity or importance. Competing Interests Policy Provide sufficient details of any financial or non-financial competing interests to enable users to assess whether your comments might lead a reasonable person to question your impartiality. Consider the following examples, but note that this is not an exhaustive list: Examples of 'Non-Financial Competing Interests' Within the past 4 years, you have held joint grants, published or collaborated with any of the authors of the selected paper. You have a close personal relationship (e.g. parent, spouse, sibling, or domestic partner) with any of the authors. You are a close professional associate of any of the authors (e.g. scientific mentor, recent student). You work at the same institute as any of the authors. You hope/expect to benefit (e.g. favour or employment) as a result of your submission. You are an Editor for the journal in which the article is published. Examples of 'Financial Competing Interests' You expect to receive, or in the past 4 years have received, any of the following from any commercial organisation that may gain financially from your submission: a salary, fees, funding, reimbursements. You expect to receive, or in the past 4 years have received, shared grant support or other funding with any of the authors. You hold, or are currently applying for, any patents or significant stocks/shares relating to the subject matter of the paper you are commenting on. Please state your competing interests The comment has been saved. An error has occurred. Please try again. Cancel Post var lTitle = "On solving system of differential-algebraic...".replace("'", ''); var linkedInUrl = "http://www.linkedin.com/shareArticle?url=https://f1000research.com/articles/12-1337/v2" + "&title=" + encodeURIComponent(lTitle) + "&summary=" + encodeURIComponent('Read the article by '); var deliciousUrl = "https://del.icio.us/post?url=https://f1000research.com/articles/12-1337/v2&title=" + encodeURIComponent(lTitle); var redditUrl = "http://reddit.com/submit?url=https://f1000research.com/articles/12-1337/v2" + "&title=" + encodeURIComponent(lTitle); linkedInUrl += encodeURIComponent('Thota S and P S'); var offsetTop = /chrome/i.test( navigator.userAgent ) ? 4 : -10; var addthis_config = { ui_offset_top: offsetTop, services_compact : "facebook,twitter,www.linkedin.com,www.mendeley.com,reddit.com", services_expanded : "facebook,twitter,www.linkedin.com,www.mendeley.com,reddit.com", services_custom : [ { name: "LinkedIn", url: linkedInUrl, icon:"/img/icon/at_linkedin.svg" }, { name: "Mendeley", url: "http://www.mendeley.com/import/?url=https://f1000research.com/articles/12-1337/v2/mendeley", icon:"/img/icon/at_mendeley.svg" }, { name: "Reddit", url: redditUrl, icon:"/img/icon/at_reddit.svg" }, ] }; var addthis_share = { url: "https://f1000research.com/articles/12-1337", templates : { twitter : "On solving system of differential-algebraic equations using adomian.... Thota S and P S, published by " + "@F1000Research" + ", https://f1000research.com/articles/12-1337/v2" } }; if (typeof(addthis) != "undefined"){ addthis.addEventListener('addthis.ready', checkCount); addthis.addEventListener('addthis.menu.share', checkCount); } $(".f1r-shares-twitter").attr("href", "https://twitter.com/intent/tweet?text=" + addthis_share.templates.twitter); $(".f1r-shares-facebook").attr("href", "https://www.facebook.com/sharer/sharer.php?u=" + addthis_share.url); $(".f1r-shares-linkedin").attr("href", addthis_config.services_custom[0].url); $(".f1r-shares-reddit").attr("href", addthis_config.services_custom[2].url); $(".f1r-shares-mendelay").attr("href", addthis_config.services_custom[1].url); function checkCount(){ setTimeout(function(){ $(".addthis_button_expanded").each(function(){ var count = $(this).text(); if (count !== "" && count != "0") $(this).removeClass("is-hidden"); else $(this).addClass("is-hidden"); }); }, 1000); } close How to cite this report {{reportCitation}} Cancel Copy Citation Details $(function(){R.ui.buttonDropdowns('.dropdown-for-downloads');}); $(function(){R.ui.toolbarDropdowns('.toolbar-dropdown-for-downloads');}); $.get("/articles/acj/140257/161819") new F1000.Clipboard(); new F1000.ThesaurusTermsDisplay("articles", "article", "161819"); $(document).ready(function() { $( "#frame1" ).on('load', function() { var mydiv = $(this).contents().find("div"); var h = mydiv.height(); console.log(h) }); var tooltipLivingFigure = jQuery(".interactive-living-figure-label .icon-more-info"), titleLivingFigure = tooltipLivingFigure.attr("title"); tooltipLivingFigure.simpletip({ fixed: true, position: ["-115", "30"], baseClass: 'small-tooltip', content:titleLivingFigure + " " }); tooltipLivingFigure.removeAttr("title"); $("body").on("click", ".cite-living-figure", function(e) { e.preventDefault(); var ref = $(this).attr("data-ref"); $(this).closest(".living-figure-list-container").find("#" + ref).fadeIn(200); }); $("body").on("click", ".close-cite-living-figure", function(e) { e.preventDefault(); $(this).closest(".popup-window-wrapper").fadeOut(200); }); $(document).on("mouseup", function(e) { var metricsContainer = $(".article-metrics-popover-wrapper"); if (!metricsContainer.is(e.target) && metricsContainer.has(e.target).length === 0) { $(".article-metrics-close-button").click(); } }); var articleId = $('#articleId').val(); if($("#main-article-count-box").attachArticleMetrics) { $("#main-article-count-box").attachArticleMetrics(articleId, { articleMetricsView: true }); } }); var figshareWidget = $(".new_figshare_widget"); if (figshareWidget.length > 0) { window.figshare.load("f1000", function(Widget) { // Select a tag/tags defined in your page. In this tag we will place the widget. _.map(figshareWidget, function(el){ var widget = new Widget({ articleId: $(el).attr("figshare_articleId") //height:300 // this is the height of the viewer part. [Default: 550] }); widget.initialize(); // initialize the widget widget.mount(el); // mount it in a tag that's on your page // this will save the widget on the global scope for later use from // your JS scripts. This line is optional. //window.widget = widget; }); }); } close Error Close Add Reset F1000.MICROSERVICES.AFFILIATION = ''; $(document).ready(function () { $('.js-affiliations-form').each((index, form) => { new AffiliationForm({ formId: form.id, institutionErrorSelector: '.comment-enter-institution', departmentErrorSelector: '.comment-enter-department', placeSelector: '.js-add-comment-place', stateSelector: '.js-add-comment-state', zipCodeSelector: '.js-add-comment-zipcode', countrySelector: '.js-add-comment-country', countryErrorSelector: '.comment-enter-country', }); }); }); $(document).ready(function () { var reportIds = { "243843": 0, "243842": 0, "243841": 0, "243840": 0, "229703": 0, "243846": 0, "243845": 0, "243844": 0, "217355": 0, "229707": 0, "217354": 0, "229706": 0, "217353": 0, "229705": 0, "229704": 0, "229711": 0, "229710": 0, "217357": 0, "217356": 0, "229708": 0, "229714": 0, "229713": 0, "259179": 0, "259178": 0, "259177": 0, "259183": 0, "259182": 0, "259181": 0, "259180": 0, "340778": 0, "259187": 0, "259185": 0, "259184": 0, "243839": 8, "243838": 0, "243837": 36, }; $(".referee-response-container,.js-referee-report").each(function(index, el) { var reportId = $(el).attr("data-reportid"), reportCount = reportIds[reportId] || 0; $(el).find(".comments-count-container,.js-referee-report-views").html(reportCount); }); var uuidInput = $("#article_uuid"), oldUUId = uuidInput.val(), newUUId = "1f9c782f-8ec6-49b7-89e0-c2b21295900e"; uuidInput.val(newUUId); $("a[href*='article_uuid=']").each(function(index, el) { var newHref = $(el).attr("href").replace(oldUUId, newUUId); $(el).attr("href", newHref); }); }); An innovative open access publishing platform offering rapid publication and open peer review, whilst supporting data deposition and sharing. Browse Gateways Collections How it Works Contact For Developers Cookie Notice Privacy Notice RSS Submit Your Research Follow us © 2012-2026 F1000 Research Ltd. ISSN 2046-1402 | Legal | Partner of Research4Life • CrossRef • ORCID • FAIRSharing R.templateTests.simpleTemplate = R.template(' $text $text $text $text $text '); R.templateTests.runTests(); var F1000platform = new F1000.Platform({ name: "f1000research", displayName: "F1000Research", hostName: "f1000research.com", id: "1", editorialEmail: "[email protected]", infoEmail: "[email protected]", usePmcStats: true }); $(function(){R.ui.dropdowns('.dropdown-for-authors, .dropdown-for-about, .dropdown-for-myresearch');}); // $(function(){R.ui.dropdowns('.dropdown-for-referees');}); $(document).ready(function () { if ($(".cookie-warning").is(":visible")) { $(".sticky").css("margin-bottom", "35px"); $(".devices").addClass("devices-and-cookie-warning"); } $(".cookie-warning .close-button").click(function (e) { $(".devices").removeClass("devices-and-cookie-warning"); $(".sticky").css("margin-bottom", "0"); }); $("#tweeter-feed .tweet-message").each(function (i, message) { var self = $(message); self.html(linkify(self.html())); }); $(".partner").on("mouseenter mouseleave", function() { $(this).find(".gray-scale, .colour").toggleClass("is-hidden"); }); }); Sign In Remember me Forgotten your password? Sign In Cancel Email or password not correct. Please try again Please wait... $(function(){ // Note: All the setup needs to run against a name attribute and *not* the id due the clonish // nature of facebox... $("a[id=googleSignInButton]").click(function(event){ event.preventDefault(); $("input[id=oAuthSystem]").val("GOOGLE"); $("form[id=oAuthForm]").submit(); }); $("a[id=facebookSignInButton]").click(function(event){ event.preventDefault(); $("input[id=oAuthSystem]").val("FACEBOOK"); $("form[id=oAuthForm]").submit(); }); $("a[id=orcidSignInButton]").click(function(event){ event.preventDefault(); $("input[id=oAuthSystem]").val("ORCID"); $("form[id=oAuthForm]").submit(); }); }); If you've forgotten your password, please enter your email address below and we'll send you instructions on how to reset your password. The email address should be the one you originally registered with F1000. Email address not valid, please try again You registered with F1000 via Google, so we cannot reset your password. To sign in, please click here . If you still need help with your Google account password, please click here . You registered with F1000 via Facebook, so we cannot reset your password. To sign in, please click here . If you still need help with your Facebook account password, please click here . Code not correct, please try again Reset password Cancel Email us for further assistance. Server error, please try again. If your email address is registered with us, we will email you instructions to reset your password. If you think you should have received this email but it has not arrived, please check your spam filters and/or contact for further assistance. Please wait... Register $(document).ready(function () { signIn.createSignInAsRow($("#sign-in-form-gfb-popup")); $(".target-field").each(function () { var uris = $(this).val().split("/"); if (uris.pop() === "login") { $(this).val(uris.toString().replace(",","/")); } }); });