@Article{JCM-21-6,
author = {Tian, Hong-Jiong},
title = {Dissipativity and Exponential Stability of $\theta$-Methods for Singularly Perturbed Delay Differential Equations with a Bounded Lag},
journal = {Journal of Computational Mathematics},
year = {2003},
volume = {21},
number = {6},
pages = {715--726},
abstract = {<p style="text-align: justify;">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 $\epsilon&gt;0$. 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 $\epsilon&gt;0$ if and only if $\theta=1$.</p>},
issn = {1991-7139},
doi = {https://doi.org/2003-JCM-8892},
url = {https://global-sci.com/article/85368/dissipativity-and-exponential-stability-of-theta-methods-for-singularly-perturbed-delay-differential-equations-with-a-bounded-lag}
}