{"title":"Estimating the growth of solutions of linear delayed difference and differential equations by alternating maximization","authors":"Miloud Sadkane , Roger B. Sidje","doi":"10.1016/j.apnum.2025.02.008","DOIUrl":null,"url":null,"abstract":"<div><div>Numerical methods are proposed to quantify the magnitude of the growth reachable by solutions of systems of delayed linear difference and differential equations that are assumed to be asymptotically stable. A foundation based on an alternating maximization algorithm is established to address the discrete-time case. Following that, it is shown how to reuse this foundation for the continuous-time case, by converting to the discrete-time case through an approximation scheme that uses a backward differentiation formula (BDF) to produce a discretization in time. This indirect conversion approach raises new theoretical questions that are examined thoroughly. The proposed methods apply to systems with constant or variable coefficients. Numerical experiments are included to demonstrate their performance and reliability on several examples.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 254-267"},"PeriodicalIF":2.2000,"publicationDate":"2025-02-17","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/S0168927425000339","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Numerical methods are proposed to quantify the magnitude of the growth reachable by solutions of systems of delayed linear difference and differential equations that are assumed to be asymptotically stable. A foundation based on an alternating maximization algorithm is established to address the discrete-time case. Following that, it is shown how to reuse this foundation for the continuous-time case, by converting to the discrete-time case through an approximation scheme that uses a backward differentiation formula (BDF) to produce a discretization in time. This indirect conversion approach raises new theoretical questions that are examined thoroughly. The proposed methods apply to systems with constant or variable coefficients. Numerical experiments are included to demonstrate their performance and reliability on several examples.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
