Asymptotical stability of numerical methods with constant stepsize for pantograph equations

被引：31

作者：

Liu, MZ ^{[1
]}

Yang, ZW

Hu, GD

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Harbin Inst Technol, Dept Control Sci & Engn, Harbin 150001, Peoples R China

来源：

BIT NUMERICAL MATHEMATICS | 2005年 / 45卷 / 04期

关键词：

pantograph equation; Razumikhin type theorem; asymptotical stability; numerical methods;

D O I：

10.1007/s10543-005-0022-3

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper, the asymptotical stability of the analytic solution and the numerical methods with constant stepsize for pantograph equations is investigated using the Razumikhin technique. In particular, the linear pantograph equations with constant coefficients and variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the theta-methods with constant stepsize are obtained. As a result Z. Jackiewicz's conjecture is partially proved. Finally, some experiments are given.

引用

页码：743 / 759

页数：17

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