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中立型比例延迟微分系统线性θ-方法的渐近估计

张根根1, 肖爱国1, 王晚生2   

  1. 1 湘潭大学数学与计算科学学院, 湘潭 411105;
    2 上海师范大学数理学院, 上海 200234
  • 收稿日期:2018-11-01 出版日期:2020-11-15 发布日期:2020-11-15
  • 基金资助:

    国家自然科学基金(11671343,11771060,11701110)资助.

张根根, 肖爱国, 王晚生. 中立型比例延迟微分系统线性θ-方法的渐近估计[J]. 计算数学, 2020, 42(4): 419-434.

Zhang Gengen, Xiao Aiguo, Wang Wansheng. THE ASYMPTOTIC ESTIMATE OF LINEAR θ-METHODS FOR SYSTEM OF NEUTRAL PANTOGRAPH DELAY DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2020, 42(4): 419-434.

THE ASYMPTOTIC ESTIMATE OF LINEAR θ-METHODS FOR SYSTEM OF NEUTRAL PANTOGRAPH DELAY DIFFERENTIAL EQUATIONS

Zhang Gengen1, Xiao Aiguo1, Wang Wansheng2   

  1. 1 School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China;
    2 Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
  • Received:2018-11-01 Online:2020-11-15 Published:2020-11-15
本文研究了一类线性非自治中立型比例延迟微分系统线性θ-方法的渐近稳定性,并借助于泛函不等式得到了数值解的渐近估计.此渐近估计不仅比数值渐近稳定性描述得更加精确,而且还能给出非稳定情形数值解的上界估计式.数值算例验证了相关理论结果.
In this paper, we investigate the asymptotic stability of linear θ-methods for a class of the linear nonautonomous neutral differential equations with pantograph delay and obtain the asymptotic estimation of numerical solution with the aid of a functional inequality. Asymptotic estimates not only describe more accurately the asymptotic behaviour for stable systems, but also give an upper bound estimate of the solution for unstable case. Numerical examples validate the theoretical results.

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