High-Performance Damped Traub-Type Iterative Scheme for Nonlinear Systems

High-Performance Damped Traub-Type Iterative Scheme for Nonlinear Systems | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 20 August 2025 V1 Latest version Share on High-Performance Damped Traub-Type Iterative Scheme for Nonlinear Systems Authors : Alicia Cordero 0000-0002-7462-9173 , Renso V. Rojas-Hiciano , Juan R. Torregrosa [email protected] , and María Vassileva Authors Info & Affiliations https://doi.org/10.22541/au.175568773.38658993/v1 209 views 198 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We present a new scheme for solving nonlinear systems that combines simplicity with high performance, offering minimal evaluation cost for an arbitrary number of steps. Given the specified assumptions, we provide its development and a convergence analysis, guaranteeing that the order is twice the number of linear systems or steps. Based on this, we introduce a new eighth-order method with low computational cost, requiring only four linear systems that share the same Jacobian matrix and scalar weight function. Efficiency studies show that this new, high-order method competes effectively with other efficient schemes in the literature. A brief real-dynamics study confirms the scheme's superior stability, covering large, connected convergence regions. Finally, numerical tests validate the theoretical results. The contribution of this work is to enable the use of very high-order schemes with low computational costs, opening new avenues for their practical application. Supplementary Material File (0.high-performance damped traub-type iterative scheme for nonlinear systems.pdf) Download 549.48 KB Information & Authors Information Version history V1 Version 1 20 August 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords damped traub-type high-order iterative methods high-performance schemes iterative methods nonlinear systems pdes Authors Affiliations Alicia Cordero 0000-0002-7462-9173 Universitat Politecnica de Valencia Institut de Matematica Multidisciplinar View all articles by this author Renso V. Rojas-Hiciano Pontificia Universidad Catolica Madre y Maestra - Campus Santo Tomas de Aquino View all articles by this author Juan R. Torregrosa [email protected] Universitat Politecnica de Valencia Institut de Matematica Multidisciplinar View all articles by this author María Vassileva Instituto Tecnologico de Santo Domingo View all articles by this author Metrics & Citations Metrics Article Usage 209 views 198 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Alicia Cordero, Renso V. Rojas-Hiciano, Juan R. Torregrosa, et al. High-Performance Damped Traub-Type Iterative Scheme for Nonlinear Systems. Authorea . 20 August 2025. DOI: https://doi.org/10.22541/au.175568773.38658993/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); Cited by Tugal Zhanlav, Khuder Otgondorj, Fully explicit and super-efficient iterative methods for solving systems of nonlinear equations, Mongolian Mathematical Journal, 26 , (42-55), (2025). https://doi.org/10.5564/mmj.v26i1.5263 Crossref Tugal Zhanlav, Khuder Otgondorj, Khangai Enkhbayar, A family of the best iterative methods for systems of nonlinear equations, Mongolian Mathematical Journal, 26 , (1-19), (2025). https://doi.org/10.5564/mmj.v26i1.5002 Crossref Loading... View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.175568773.38658993/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9fed9a1ce88c0db4',t:'MTc3OTMwMzgxMg=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();