摘要
1.引言
现有文献中对于非线性延迟微分方程渐近稳定性及其数值方法的稳定性研究大都有局限于常延迟的情形,例如可参见匡咬勋[1-3],黄乘明[4],Torelli[5]等人的大量工作.
In this paper, we discuss the asymptotic stability of nonlinear Delay Differential Equations(DDEs) with a variable delay and the numerical stability of one-leg methods when applied to such equations. At first, we give a sufficient condition for the aforementioned equations to be asymptotic stable, which is simpler and more effective than that presented by Zennaro in 1997. For one-leg methods applied to nonlinear DDEs with a variable delay, we introduce a series of new stability concepts, such as GR(v)-stability, GAR(v)-stability and weak GAR(v)-stability, where v > 0 is a given constant. Afterwards, for one-leg methods with linear interpolation, we prove that A-stability implies GR(2^(1/2)/2)-stability and weak GAR(2^(1/2)/2)-stability, and that strong A-stability implies GAR(2^(1/2)/2)-stability for delay differential equations with a variable delay. Several numerical tests listed at the end of this paper to confirm the above theoretical results.
出处
《计算数学》
CSCD
北大核心
2002年第4期417-430,共14页
Mathematica Numerica Sinica
基金
国家863高技术惯性约束聚变主题资助科研项目
湖南省教育厅资助科研项目.
关键词
非线性刚性变延迟微分方程
单支方法
渐近稳定性
数值稳定性
Nonlinear stiff delay differential equations with a variable delay, one-leg methods, asymptotic stability, numerical stability
