Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) plus a0u([t])

被引：38

作者：

Liu, MZ ^{[1
]}

Song, MH ^{[1
]}

Yang, ZW ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2004年 / 166卷 / 02期

基金：

中国国家自然科学基金;

关键词：

delay differential equation; piecewise continuous arguments; asymptotic stability;

D O I：

10.1016/j.cam.2003.04.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the stability analysis of the Runge-Kutta methods for the equation u'(t)=au(t)+a(0)u([t]). The stability regions for the Runge-Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given. (C) 2003 Published by Elsevier B.V.

引用

页码：361 / 370

页数：10

共 13 条

[1]

[Anonymous], 1984, DIFF EQUAT+

[2]

Busenberg S, 1982, NONLINEAR PHENOMENA, P179

[3]

Butcher J. C., 1987, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods

[4] RETARDED DIFFERENTIAL-EQUATIONS WITH PIECEWISE CONSTANT DELAYS [J].

COOKE, KL ;

WIENER, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1984, 99 (01) :265-297

[5]

Dekker K, 1984, STABILITY RUNGE KUTT

[6]

Hairer E., 1993, SOLVING ORDINARY DIF, VII

[7] ORDER STARS AND RATIONAL APPROXIMANTS TO EXP(Z) [J].

ISERLES, A ;

NORSETT, SP .

APPLIED NUMERICAL MATHEMATICS, 1989, 5 (1-2) :63-70

[8]

KOCIC VL, 1993, GLOBAL BEHAV NONLINE

[9]

Lakshmikantham V., 1983, Trends in the Theory and Practice of Nonlinear Differential Equations, P547

[10] Global stability and chaos in a population model with piecewise constant arguments [J].

Liu, PZ ;

Gopalsamy, K .

APPLIED MATHEMATICS AND COMPUTATION, 1999, 101 (01) :63-88

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