Stabilities of (A,B,C) and NPDIRK Methods for Systems of Neutral Delay-Differential Equations with Multiple Delays

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.

Author Details

Guo-Feng Zhang