Conditional contractivity of Runge-Kutta methods for nonlinear differential equations with many variable delays

被引：6

作者：

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

Li, Shou-Fu ^{[2
]}

机构：

[1] Changsha Univ Sci & Technol, Sch Math & Computat Sci, Changsha 410076, Hunan, Peoples R China

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

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2009年 / 14卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Nonlinear delay differential equations; Runge-Kutta methods; Contractivity; Conditional contractivity; GENERAL LINEAR METHODS; ASYMPTOTIC STABILITY; NUMERICAL-METHODS; B-THEORY; SYSTEMS;

D O I：

10.1016/j.cnsns.2007.09.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with conditional contractivity properties of Runge-Kutta (RK) methods with variable step-size applied to nonlinear differential equations with many variable delays (MDDEs). The concepts of CRNm(omega, H)(-) and BNf (mu, h)-stability are introduced. It is shown that the numerical solution produced by a BNf (mu, h)-stable Runge-Kutta method with an appropriate interpolation is contractive. In particular, these results are also novel for nonlinear differential equations with many constant delays or single variable delay. To obtain BNf (mu, h)-stable methods, (k, l)-algebraically stable Runge-Kutta methods are also investigated. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：399 / 408

页数：10

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