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.
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页数：13
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