{"title":"Numerical solutions of stochastic delay integro-differential equations by block pulse functions","authors":"Guo Jiang, Yuanqin Chen, Jiayi Ying","doi":"10.1016/j.apnum.2024.10.017","DOIUrl":null,"url":null,"abstract":"<div><div>This paper presents an efficient numerical method for solving nonlinear stochastic delay integro-differential equations based on block pulse functions. Firstly, the equation is transformed into an algebraic system by the integral delay operator matrixes of block pulse functions. Then, error analysis is conducted on the method. Finally, some numerical examples are provided to validate the method. This work provides numerical solutions for the stochastic delay integro-differential equations by global approximation method. This method has the advantages of simple calculation and higher error accuracy.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 214-230"},"PeriodicalIF":2.4000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424002939","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/30 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents an efficient numerical method for solving nonlinear stochastic delay integro-differential equations based on block pulse functions. Firstly, the equation is transformed into an algebraic system by the integral delay operator matrixes of block pulse functions. Then, error analysis is conducted on the method. Finally, some numerical examples are provided to validate the method. This work provides numerical solutions for the stochastic delay integro-differential equations by global approximation method. This method has the advantages of simple calculation and higher error accuracy.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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