• 论文 •

### 非线性刚性变延迟微分方程单支方法的数值稳定性

1. 湘潭大学计算与应用数学研究所,湘潭大学计算与应用数学研究所 湖南湘潭,411105 ,湖南湘潭,411105
• 出版日期:2002-04-14 发布日期:2002-04-14

### THE NUMERICAL STABILITY OF ONE-LEG METHODS FOR NONLINEAR STIFF DELAY DIFFERENTIAL EQUATIONS WITH A VARIABLE DELAY

1. Wang Wenqiang Li Shoufu(Institute for Computational and Applied Mathematics, Xiangtan University,Xiangtan, Hunan, 411105)
• Online:2002-04-14 Published:2002-04-14

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.
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