求解时滞微分方程的对角隐式二阶导数Runge-Kutta方法的稳定性分析

IF 0.5 Q3 MATHEMATICS

Malaysian Journal of Mathematical Sciences Pub Date : 2022-04-29 DOI:10.47836/mjms.16.2.04

N. A. Ahmad, N. Senu, Z. Ibrahim, M. Othman

{"title":"求解时滞微分方程的对角隐式二阶导数Runge-Kutta方法的稳定性分析","authors":"N. A. Ahmad, N. Senu, Z. Ibrahim, M. Othman","doi":"10.47836/mjms.16.2.04","DOIUrl":null,"url":null,"abstract":"The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative Runge-Kutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their stability regions for (λ,μ∈R) and (μ∈C,λ=0) are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit Runge-Kutta (DIRK) methods when solving DDEs problems are clearly demonstrated by plotting the efficiency curves of the log of both maximum errors versus function evaluations and the CPU time taken to do the integration.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations\",\"authors\":\"N. A. Ahmad, N. Senu, Z. Ibrahim, M. Othman\",\"doi\":\"10.47836/mjms.16.2.04\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative Runge-Kutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their stability regions for (λ,μ∈R) and (μ∈C,λ=0) are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit Runge-Kutta (DIRK) methods when solving DDEs problems are clearly demonstrated by plotting the efficiency curves of the log of both maximum errors versus function evaluations and the CPU time taken to do the integration.\",\"PeriodicalId\":43645,\"journal\":{\"name\":\"Malaysian Journal of Mathematical Sciences\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Malaysian Journal of Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47836/mjms.16.2.04\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Malaysian Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47836/mjms.16.2.04","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

研究了四阶和五阶对角隐式二阶导数龙格-库塔方法（DITDRK）与拉格朗日插值相结合应用于线性时滞微分方程（DDE）的稳定性。这种类型的稳定性被称为P-稳定性和Q-稳定性。确定了（λ，μ∈R）和（μ∈C，λ=0）的稳定域。DITDRK方法在解决DDE问题时优于其他同阶现有的对角隐式龙格-库塔（DIRK）方法，这一点通过绘制最大误差对数与函数评估和积分所需CPU时间的效率曲线得到了清楚的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations

The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative Runge-Kutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their stability regions for (λ,μ∈R) and (μ∈C,λ=0) are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit Runge-Kutta (DIRK) methods when solving DDEs problems are clearly demonstrated by plotting the efficiency curves of the log of both maximum errors versus function evaluations and the CPU time taken to do the integration.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Malaysian Journal of Mathematical Sciences MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.