A generic numerical method for treating a system of Volterra integro-differential equations with multiple delays and variable bounds

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Ömür Kıvanç Kürkçü, Mehmet Sezer
{"title":"A generic numerical method for treating a system of Volterra integro-differential equations with multiple delays and variable bounds","authors":"Ömür Kıvanç Kürkçü, Mehmet Sezer","doi":"10.1108/ec-09-2023-0590","DOIUrl":null,"url":null,"abstract":"<h3>Purpose</h3>\n<p>This study aims to treat a novel system of Volterra integro-differential equations with multiple delays and variable bounds, constituting a generic numerical method based on the matrix equation and a combinatoric-parametric Charlier polynomials. The proposed method utilizes these polynomials for the matrix relations at the collocation points.</p><!--/ Abstract__block -->\n<h3>Design/methodology/approach</h3>\n<p>Thanks to the combinatorial eligibility of the method, the functional terms can be transformed into the generic matrix relations with low dimensions, and their resulting matrix equation. The obtained solutions are tested with regard to the parametric behaviour of the polynomials with $\\alpha$, taking into account the condition number of an outcome matrix of the method. Residual error estimation improves those solutions without using any external method. A calculation of the residual error bound is also fulfilled.</p><!--/ Abstract__block -->\n<h3>Findings</h3>\n<p>All computations are carried out by a special programming module. The accuracy and productivity of the method are scrutinized via numerical and graphical results. Based on the discussions, one can point out that the method is very proper to solve a system in question.</p><!--/ Abstract__block -->\n<h3>Originality/value</h3>\n<p>This paper introduces a generic computational numerical method containing the matrix expansions of the combinatoric Charlier polynomials, in order to treat the system of Volterra integro-differential equations with multiple delays and variable bounds. Thus, the method enables to evaluate stiff differential and integral parts of the system in question. That is, these parts generates two novel components in terms of unknown terms with both differentiated and delay arguments. A rigorous error analysis is deployed via the residual function. Four benchmark problems are solved and interpreted. Their graphical and numerical results validate accuracy and efficiency of the proposed method. In fact, a generic method is, thereby, provided into the literature.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Computations","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1108/ec-09-2023-0590","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

Abstract

Purpose

This study aims to treat a novel system of Volterra integro-differential equations with multiple delays and variable bounds, constituting a generic numerical method based on the matrix equation and a combinatoric-parametric Charlier polynomials. The proposed method utilizes these polynomials for the matrix relations at the collocation points.

Design/methodology/approach

Thanks to the combinatorial eligibility of the method, the functional terms can be transformed into the generic matrix relations with low dimensions, and their resulting matrix equation. The obtained solutions are tested with regard to the parametric behaviour of the polynomials with $\alpha$, taking into account the condition number of an outcome matrix of the method. Residual error estimation improves those solutions without using any external method. A calculation of the residual error bound is also fulfilled.

Findings

All computations are carried out by a special programming module. The accuracy and productivity of the method are scrutinized via numerical and graphical results. Based on the discussions, one can point out that the method is very proper to solve a system in question.

Originality/value

This paper introduces a generic computational numerical method containing the matrix expansions of the combinatoric Charlier polynomials, in order to treat the system of Volterra integro-differential equations with multiple delays and variable bounds. Thus, the method enables to evaluate stiff differential and integral parts of the system in question. That is, these parts generates two novel components in terms of unknown terms with both differentiated and delay arguments. A rigorous error analysis is deployed via the residual function. Four benchmark problems are solved and interpreted. Their graphical and numerical results validate accuracy and efficiency of the proposed method. In fact, a generic method is, thereby, provided into the literature.

处理具有多重延迟和变量边界的 Volterra 积分微分方程系统的通用数值方法
目的本研究旨在处理一个具有多重延迟和变量边界的新型 Volterra 积分微分方程系统,构成一种基于矩阵方程和组合参数 Charlier 多项式的通用数值方法。设计/方法/途径由于该方法的组合资格,函数项可以转化为低维度的通用矩阵关系,以及由此产生的矩阵方程。在考虑到该方法结果矩阵的条件数的情况下,对所获得的解决方案进行了$\α$多项式参数行为测试。残余误差估计无需使用任何外部方法即可改进这些解。所有计算均由一个特殊的编程模块完成。所有计算均由一个专门的编程模块完成,并通过数值和图形结果对该方法的准确性和效率进行了仔细检查。原创性/价值 本文介绍了一种通用计算数值方法,该方法包含组合夏利耶多项式的矩阵展开,用于处理具有多重延迟和变量边界的 Volterra 微分方程系统。因此,该方法能够评估相关系统的刚性微分和积分部分。也就是说,这些部分产生了两个新的组成部分,即具有微分和延迟参数的未知项。通过残差函数进行严格的误差分析。对四个基准问题进行了求解和解释。其图形和数值结果验证了所提方法的准确性和效率。事实上,这也为文献提供了一种通用方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信