Volume 21, Issue 4
Delay-Dependent Treatment of Linear Multistep Methods for Neutral Delay Differential Equations

J. Comp. Math., 21 (2003), pp. 535-544.

Published online: 2003-08

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• Abstract

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations $y'(t) = ay(t) + by(t - \tau) + cy'(t - \tau), t > 0, y(t) = g(t), -\tau ≤ t ≤ 0, a,b$  and $c \in \mathbb{R}.$ The necessary condition for linear multistep methods to be $N_\tau(0)$-stable is given. It is shown that the trapezoidal rule is $N_\tau(0)$-compatible. Figures of stability region for some linear multistep methods are depicted.

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@Article{JCM-21-535, author = {Jaffer , Syed Khalid and Liu , Ming-Zhu}, title = {Delay-Dependent Treatment of Linear Multistep Methods for Neutral Delay Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {4}, pages = {535--544}, abstract = {

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations $y'(t) = ay(t) + by(t - \tau) + cy'(t - \tau), t > 0, y(t) = g(t), -\tau ≤ t ≤ 0, a,b$  and $c \in \mathbb{R}.$ The necessary condition for linear multistep methods to be $N_\tau(0)$-stable is given. It is shown that the trapezoidal rule is $N_\tau(0)$-compatible. Figures of stability region for some linear multistep methods are depicted.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10257.html} }
TY - JOUR T1 - Delay-Dependent Treatment of Linear Multistep Methods for Neutral Delay Differential Equations AU - Jaffer , Syed Khalid AU - Liu , Ming-Zhu JO - Journal of Computational Mathematics VL - 4 SP - 535 EP - 544 PY - 2003 DA - 2003/08 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10257.html KW - Delay-dependent stability, Linear multistep methods, Neutral delay differential equations. AB -

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations $y'(t) = ay(t) + by(t - \tau) + cy'(t - \tau), t > 0, y(t) = g(t), -\tau ≤ t ≤ 0, a,b$  and $c \in \mathbb{R}.$ The necessary condition for linear multistep methods to be $N_\tau(0)$-stable is given. It is shown that the trapezoidal rule is $N_\tau(0)$-compatible. Figures of stability region for some linear multistep methods are depicted.

Syed Khalid Jaffer & Ming-Zhu Liu. (1970). Delay-Dependent Treatment of Linear Multistep Methods for Neutral Delay Differential Equations. Journal of Computational Mathematics. 21 (4). 535-544. doi:
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