Stability of Runge-Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments

被引：8

作者：

Lv, W. J. ^{[1
]}

Yang, Z. W. ^{[1
]}

Liu, M. Z. ^{[1
]}

机构：

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2007年 / 54卷 / 03期

基金：

中国国家自然科学基金;

关键词：

alternately advanced and retarded differential equations; piecewise continuous arguments; asymptotical stability;

D O I：

10.1016/j.camwa.2006.07.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the numerical properties of Runge-Kutta methods for the solution of u'(t) = au(t) + a(0)u([t + 1/2]). It is shown that the Runge-Kutta method can preserve the convergence order. The necessary and sufficient conditions under which the analytical stability region is contained in the numerical stability region are obtained. It is interesting that the theta-methods with 0 <= theta < 1/2 are asymptotically stable. Some numerical experiments are given. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：326 / 335

页数：10

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