Stabilities of (A,B,C) and NPDIRK Methods for Systems of Neutral Delay-Differential Equations with Multiple Delays
Year: 2003
Author: Guo-Feng Zhang
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 3 : pp. 375–382
Abstract
Consider the following neutral delay-differential equations with multiple delays (NMDDE)$$y'(t)=Ly(t)+\sum_{j=1}^{m}[M_jy(t-\tau_j)+N_jy'(t-\tau_j)],\ \ t\geq 0, (0.1)$$ where $\tau>0$, $L, M_j$ 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'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).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-10266
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 3 : pp. 375–382
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Neutral delay differential equations (A B C)-method RK method Parallel diagonally-implicit iteration RK method.