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 - <p style="text-align: justify;">This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations $y&#39;(t) = ay(t) + by(t - \tau) + cy&#39;(t - \tau), t &gt; 0, y(t) = g(t), -\tau ≤ t ≤ 0, a,b$&nbsp; and $c \in&nbsp; \mathbb{R}.$ 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.</p>