Nonlinear stability of one-leg methods for delay differential equations of neutral type

被引：35

作者：

Wang, Wan-Sheng ^{[1
,2
]}

Zhang, Yuan ^{[1
]}

Li, Shou-Fu ^{[1
]}

机构：

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

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

来源：

APPLIED NUMERICAL MATHEMATICS | 2008年 / 58卷 / 02期

基金：

中国国家自然科学基金;

关键词：

nonlinear neutral delay differential equations; one-leg methods; numerical stability; A-stability;

D O I：

10.1016/j.apnum.2006.11.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to investigations into numerical stability properties of one-leg methods for nonlinear neutral delay differential equations. At first, a series of new stability concepts, such as GS-stability, GAS-stability, and Weak GS-stability, are introduced. Then it is proved that a strongly A-stable one-leg method with linear interpolation is GAS-stable, and that an A-stable one-leg method with linear interpolation is GS-stable and Weakly GS-stable. Some numerical experiments are given in the last section of this paper which confirm our results. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：122 / 130

页数：9

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