TY - JOUR
T1 - Dissipativity and Exponential Stability of $\theta$-Methods for Singularly Perturbed Delay Differential Equations with a Bounded Lag
AU - Tian , Hong-Jiong
JO - Journal of Computational Mathematics
VL - 6
SP - 715
EP - 726
PY - 2003
DA - 2003/12
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8892.html
KW - Singular perturbation, $\theta-$methods, Dissipativity, Exponential stability.
AB - <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>