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Volume 21, Issue 6
Dissipativity and Exponential Stability of $\theta$-Methods for Singularly Perturbed Delay Differential Equations with a Bounded Lag

Hong-Jiong Tian

J. Comp. Math., 21 (2003), pp. 715-726.

Published online: 2003-12

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  • 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 $\theta=1$.

  • Keywords

Singular perturbation, $\theta-$methods, Dissipativity, Exponential stability.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-715, 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 = {

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 $\theta=1$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8892.html} }
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 -

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 $\theta=1$.

Tian , Hong-Jiong. (2003). Dissipativity and Exponential Stability of $\theta$-Methods for Singularly Perturbed Delay Differential Equations with a Bounded Lag. Journal of Computational Mathematics. 21 (6). 715-726. doi:
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