@Article{JCM-21-3,
author = {Zhang, Guo-Feng},
title = {Stabilities of (A,B,C) and NPDIRK Methods for Systems of Neutral Delay-Differential Equations with Multiple Delays},
journal = {Journal of Computational Mathematics},
year = {2003},
volume = {21},
number = {3},
pages = {375--382},
abstract = {<p style="text-align: justify;">Consider the following neutral delay-differential equations with multiple delays (NMDDE)$$y&#39;(t)=Ly(t)+\sum_{j=1}^{m}[M_jy(t-\tau_j)+N_jy&#39;(t-\tau_j)],\ \ t\geq 0,&nbsp; &nbsp; &nbsp;(0.1)$$ where $\tau&gt;0$, $L, M_j$ and $N_j$ are constant complex- value $d×d$ matrices. A sufficient condition for the asymptotic stability of NMDDE system (0.1) is given. The stability of Butcher&#39;s (A,B,C)-method for systems of NMDDE is studied. In addition, we present a parallel diagonally-implicit iteration RK (PDIRK) methods (NPDIRK) for systems of NMDDE, which is easier to be implemented than fully implicit RK methos. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1).</p>},
issn = {1991-7139},
doi = {https://doi.org/2003-JCM-10266},
url = {https://global-sci.com/article/85330/stabilities-of-abc-and-npdirk-methods-for-systems-of-neutral-delay-differential-equations-with-multiple-delays}
}