Nonlinear stability of Runge-Kutta methods applied to infinite delay differential equation
Zhang, CJ; Sun, G
AbstractIn 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.
Keywordnonlinear stability Runge-Kutta methods infinite-delay-differential equations
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Interdisciplinary Applications ; Computer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000220684900010
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Document Type期刊论文
Corresponding AuthorZhang, CJ
Affiliation1.Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Peoples R China
2.Chinese Acad Sci, Inst Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
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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.
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