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.
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页码：122 / 130
页数：9
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