Nonlinear stability of Runge-Kutta methods applied to infinite delay differential equation

doi:10.1016/S0895-7177(04)00035-4

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	Nonlinear stability of Runge-Kutta methods applied to infinite delay differential equation
	Zhang, CJ ; Sun, G
	2004-02-01
发表期刊	MATHEMATICAL AND COMPUTER MODELLING
ISSN	0895-7177
卷号	39 期号:4-5 页码:495-503
摘要	In functional differential equations (FDEs), there is a class of infinite delay-differential equations (IDDEs) with proportional delays, which aries in many scientific fields such as electric mechanics, quantum mechanics, and optics. Ones have found that-there exist very different mathematical challenges between FDEs with proportional delays and those with constant delays. Some research on the numerical solutions and the corresponding analysis for the linear FDEs with proportional delays have been presented by-several authors. However, up to now them research for nonlinear case still remains to be done. For this, in the present paper, we deal with nonlinear stability of the Runge-Kutta (RK)methods for a class of IDDEs with proportional delays. It is shown under the suitable conditions that a (k, l)-algebraically stable RK method for this kind of nonlinear IDDE is globally and asymptotically stable. (C) 2004 Elsevier Ltd. All rights reserved.
关键词	nonlinear stability Runge-Kutta methods infinite-delay-differential equations
DOI	10.1016/S0895-7177(04)00035-4
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Interdisciplinary Applications ; Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000220684900010
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19457
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, CJ
作者单位	1.Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Peoples R China 2.Chinese Acad Sci, Inst Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, CJ,Sun, G. Nonlinear stability of Runge-Kutta methods applied to infinite delay differential equation[J]. MATHEMATICAL AND COMPUTER MODELLING,2004,39(4-5):495-503.
APA	Zhang, CJ,&Sun, G.(2004).Nonlinear stability of Runge-Kutta methods applied to infinite delay differential equation.MATHEMATICAL AND COMPUTER MODELLING,39(4-5),495-503.
MLA	Zhang, CJ,et al."Nonlinear stability of Runge-Kutta methods applied to infinite delay differential equation".MATHEMATICAL AND COMPUTER MODELLING 39.4-5(2004):495-503.