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非线性中立型延迟微分方程稳定性分析

王晚生,李寿佛   

  1. 湘潭大学数学系,湘潭大学数学系 湖南 湘潭,411105 ,湖南 湘潭,411105
  • 出版日期:2004-03-14 发布日期:2004-03-14

王晚生,李寿佛. 非线性中立型延迟微分方程稳定性分析[J]. 计算数学, 2004, 26(3): 303-314.

STABILITY ANALYSIS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

  1. Wang Wansheng Li Shoufu (Department of Mathematics, Xiangtan University, Xiangtan Hunan, 411105)
  • Online:2004-03-14 Published:2004-03-14
1.引 言 延迟微分方程广泛出现于物理,生物,工程,经济学,环境论,控制理论等领域.其算法的理论研究具有十分重要的意义,对滞后型非线性延迟微分方程研究已日趋成熟.但对中立型延迟微分方程(NDDEs)特别是其非线性数值稳定性的研究则进展缓慢.对于线性NDDEs,位作者已研究了其真解以及数值解的渐近稳定性(见[1,2,3,4]).胡广大还在[5]中对数值求解线性NDDEs的步长进行了估计,而在最近的[6]中A.Bellen等考虑了形
This paper is devoted to the stability analysis of both the true solution and the numerical approximations for nonlinear systems of neutral delay differential equa-tions(NDDEs) of the general form y'(t) = F(t, y(t), y(t-r(t)), y'(t-r(t))). We first present a sufficient condition on the stability and asymptotic stability of theoretical solution for the nonlinear systems. This work extends the results recently obtained by A.Bellen et al. for the form y'(t) = F(t,y(t),G(t,y(t-T(t)),y'(t-T(t)))). Then numerical stability of Runge-Kutta methods for the systems of neutral delay differential equations is also investigated. Several numerical tests listed at the end of this paper to confirm the above theoretical results.
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