Optimization of Numerical Solutions of Stochastic Differential Equations with Time Delay

Optimization of Numerical Solutions of Stochastic Differential Equations with Time Delay | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (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;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimization of Numerical Solutions of Stochastic Differential Equations with Time Delay Dejan Stosovic, Elvir Čajić This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3877199/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The research focuses on the optimization of numerical solutions of neutral stochastic differential equations with time delay. Analyzing approaches such as Euler-Maruyama, backward Euler, and θ -Euler-Maruyama methods, the goal is to investigate the characteristics of approximate solutions, especially stability and boundedness. This study contributes to the understanding of the complexity of stochastic processes, offering a perspective for further mathematical modeling and optimization. The study of the characteristics of approximate solutions includes a detailed analysis of their stability and limitations, providing insight into the system’s behavior in dynamic conditions. This analysis lays the foundations for the improvement of numerical methods and more precise modeling of stochastic processes with time delay. The aforementioned approaches, such as the Euler-Maruyama, backward Euler, and θ -Euler-Maruyama methods, provide tools for understanding and solving complex mathematical challenges. Through an interdisciplinary approach, this study sheds light on the field of optimization of numerical solutions, encouraging further development of theoretical and practical aspects of stochastic differential equations. Applied Mathematics Discrete Mathematics stochastic process stochastic differential equations numerical methods optimization of solutions time delay Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3877199","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267943788,"identity":"a1ff6d1a-a5a6-4cdb-9c58-1a49aafc2db5","order_by":0,"name":"Dejan Stosovic","email":"","orcid":"","institution":"Faculty of Technical Sciences, 38220 Kosovska Mitrovica, Serbia","correspondingAuthor":false,"prefix":"","firstName":"Dejan","middleName":"","lastName":"Stosovic","suffix":""},{"id":267943789,"identity":"8888e565-e055-4722-b918-88b4759ff83e","order_by":1,"name":"Elvir Čajić","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYJACgwQGGzl+ECuhgHgtacaSDSAtBsRbdDjR4ABYNxFq+dkPPyh4UJOWYHx+deKHBwYM8vxiB/BrkexJMzBIOGaTZ3bj7WYJoMMMZ85OwK/F4AaDgUFiQ1qx2Y2zG0BaEgxuE9Bif4P9A1DL4cTNM85u/kGUFgMJHgOwlg38vduIs0XiTE4B0C9pxhI3eLdZJBhIEPYLf/vxbYY/aoBR2X92880fFTby/NIEtAABGyQyJMAqJQgqBwHmBxD7DhClehSMglEwCkYgAAAhOkWfVRVKGQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-4967-6269","institution":"European University Kallos Tuzla Bosnia and Herzegovina","correspondingAuthor":true,"prefix":"","firstName":"Elvir","middleName":"","lastName":"Čajić","suffix":""}],"badges":[],"createdAt":"2024-01-19 00:36:04","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-3877199/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3877199/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49941101,"identity":"0795066f-f1da-418c-8aa5-36ddadd4df6d","added_by":"auto","created_at":"2024-01-22 02:30:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":429566,"visible":true,"origin":"","legend":"","description":"","filename":"untitledSTOSEVICLATEXPDF.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3877199/v1_covered_0a4b97fb-de13-4ed2-a9b2-3af15fbaa8dd.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimization of Numerical Solutions of Stochastic Differential Equations with Time Delay\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"stochastic process, stochastic differential equations, numerical methods, optimization of solutions, time delay","lastPublishedDoi":"10.21203/rs.3.rs-3877199/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3877199/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe research focuses on the optimization of numerical solutions of neutral stochastic differential equations with time delay. 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