TY - JOUR
T1 - The Stability of Linear Multistep Methods for Linear Systems of Neutral Differential Equations
AU - Tian , Hong-Jiong
AU - Kuang , Jiao-Xun
AU - Qiu , Lin
JO - Journal of Computational Mathematics
VL - 2
SP - 125
EP - 130
PY - 2001
DA - 2001/04
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8963.html
KW - Numerical stability, Linear multistep method, Delay differential equations.
AB - <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>