Dissipativity and Exponential Stability of $\theta$-Methods for Singularly Perturbed Delay Differential Equations with a Bounded Lag

Dissipativity and Exponential Stability of $\theta$-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 $\epsilon>0$. We will study the numerical solution defined by the linear $\theta-$method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small $\epsilon>0$ if and only if $\theta=1$.

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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 $\theta-$methods Dissipativity Exponential stability.

Author Details

Hong-Jiong Tian