{"title":"Stability analysis of explicit exponential Rosenbrock methods for stiff differential equations with constant delay","authors":"","doi":"10.1016/j.amc.2024.128978","DOIUrl":null,"url":null,"abstract":"<div><p>Delay differential equations have been used to model numerous phenomena in nature. We extend the previous work of one of the authors to analyze the stability properties of the explicit exponential Rosenbrock methods for stiff differential equations with constant delay. We first derive sufficient conditions so that the exponential Rosenbrock methods satisfy the desired stability property. We accomplish this without relying on some extreme constraints, which are usually necessary in stability analysis. Then, with the aid of the integral form of the method coefficients, we provide a simple stability criterion that can be easily verified. We also present a theorem on the order barrier for the proposed methods, stating that there is no method of order five or higher that satisfies the simple criterion. Numerical tests are carried out to validate the theoretical results.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324004399","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
Delay differential equations have been used to model numerous phenomena in nature. We extend the previous work of one of the authors to analyze the stability properties of the explicit exponential Rosenbrock methods for stiff differential equations with constant delay. We first derive sufficient conditions so that the exponential Rosenbrock methods satisfy the desired stability property. We accomplish this without relying on some extreme constraints, which are usually necessary in stability analysis. Then, with the aid of the integral form of the method coefficients, we provide a simple stability criterion that can be easily verified. We also present a theorem on the order barrier for the proposed methods, stating that there is no method of order five or higher that satisfies the simple criterion. Numerical tests are carried out to validate the theoretical results.
期刊介绍:
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.