Volume 21, Issue 3
Stabilities of (A,B,C) and NPDIRK Methods for Systems of Neutral Delay-Differential Equations with Multiple Delays
DOI:

J. Comp. Math., 21 (2003), pp. 375-382

Published online: 2003-06

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• Abstract

Consider the following neutral delay-differential equations with multiple delays (NMDDE)$$y'(t)=Ly(t)+\sum_{j=1}^{m}[M_jy(t-\tau_j)+N_jy'(t-\tau_j)],\ \ t\geq 0,\eqno(0.1)$$ 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 are 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).

• Keywords

Neutral delay differential equations (A B C)-method RK method Parallel diagonally-implicit iteration

@Article{JCM-21-375, author = {Guo-feng Zhang}, 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 = { Consider the following neutral delay-differential equations with multiple delays (NMDDE)$$y'(t)=Ly(t)+\sum_{j=1}^{m}[M_jy(t-\tau_j)+N_jy'(t-\tau_j)],\ \ t\geq 0,\eqno(0.1)$$ 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 are 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). }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10266.html} }
TY - JOUR T1 - Stabilities of (A,B,C) and NPDIRK Methods for Systems of Neutral Delay-Differential Equations with Multiple Delays AU - Guo-feng Zhang JO - Journal of Computational Mathematics VL - 3 SP - 375 EP - 382 PY - 2003 DA - 2003/06 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10266.html KW - Neutral delay differential equations KW - (A B C)-method KW - RK method KW - Parallel diagonally-implicit iteration AB - Consider the following neutral delay-differential equations with multiple delays (NMDDE)$$y'(t)=Ly(t)+\sum_{j=1}^{m}[M_jy(t-\tau_j)+N_jy'(t-\tau_j)],\ \ t\geq 0,\eqno(0.1)$$ 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 are 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).