Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach space

被引：11

作者：

Wang, Wansheng ^{[1
,2
]}

Wen, Liping ^{[2
]}

Li, Shoufu ^{[2
]}

机构：

[1] Changsha Univ Sci & Technol, Sch Math & Computat Sci, Changsha 410114, Hunan, Peoples R China

[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 233卷 / 10期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Nonlinear neutral delay differential equations; Linear multistep methods; Numerical stability; Banach space; RUNGE-KUTTA METHODS; NUMERICAL-SOLUTION; B-THEORY; SYSTEMS; CONTRACTIVITY; CONVERGENCE; FORM;

D O I：

10.1016/j.cam.2009.10.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to investigating the nonlinear stability properties of linear multistep methods for the solution to neutral delay differential equations in Banach space. Two approaches to numerically treating the "neutral term" are considered, which allow us to prove several results on numerical stability of linear multistep methods. These results provide some criteria for choosing the step size such that the numerical method is stable. Some examples of application and a numerical experiment, which further confirms the main results, are given. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：2423 / 2437

页数：15

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