Numerical stability and oscillation of the Runge-Kutta methods for equation x′(t) = ax(t) plus a0x(M[t plus N/M])

被引：1

作者：

Song, Minghui ^{[1
]}

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

机构：

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

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2012年

基金：

中国国家自然科学基金;

关键词：

stability; oscillation; differential equation; Runge-Kutta method; DIFFERENTIAL-EQUATIONS; THETA-METHODS; AU(T) PLUS; U'(T);

D O I：

10.1186/1687-1847-2012-146

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 alternately of retarded and advanced equation x '(t) = ax(t) + a(0)x(M[t+N/M]). Necessary and sufficient conditions for the stability and oscillation of the numerical solution are given. The conditions that the Runge-Kutta methods preserve the stability and oscillations of the analytic solutions are obtained. Some numerical experiments are illustrated.

引用

页数：13

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