@Article{JCM-19-2,
author = {Tian, Hong-Jiong and Kuang, Jiao-Xun and Qiu, Lin},
title = {The Stability of Linear Multistep Methods for Linear Systems of Neutral Differential Equations},
journal = {Journal of Computational Mathematics},
year = {2001},
volume = {19},
number = {2},
pages = {125--130},
abstract = {<p style="text-align: justify;">This paper deals with the numerical solution of initial value problems for systems of neutral differential equations $$y&#39;(t)=f(t,y(t),y(t- \tau ),y&#39;(t- \tau )), t ＞ 0, $$ $$y(t) = φ(t) \ t＜0,$$ where $\tau＞ 0, f$ and <span style="text-align: justify;">φ</span> denote given vector-valued functions. The numerical stability of a linear multistep method is investigated by analysing the solution of the test equations $y&#39;(t)=Ay(t) + By(t-\tau) + Cy&#39;(t-\tau),$ where $A, B$ and $C$ denote constant complex $N \times N$-matrices, and $\tau ＞ 0$. We investigate the properties of adaptation of the linear multistep method and the characterization of the stability region. It is proved that the linear multistep method is NGP-stable if and only if it is A-stable for ordinary differential equations. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/2001-JCM-8963},
url = {https://global-sci.com/article/85453/the-stability-of-linear-multistep-methods-for-linear-systems-of-neutral-differential-equations}
}