Dissipativity and Exponential Stability of θ-Methods for Singularly Perturbed Delay Differential Equations with a Bounded Lag
Year: 2003
Author: Hong-Jiong Tian
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 6 : pp. 715–726
Abstract
This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ϵ>0. We will study the numerical solution defined by the linear θ−method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ϵ>0 if and only if θ=1.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-8892
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 6 : pp. 715–726
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Singular perturbation θ−methods Dissipativity Exponential stability.
Author Details
Hong-Jiong Tian Email