STABILITIES OF (A,B,C) AND NPDIRK METHODS FOR SYSTEMS OF NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS

作     者：Guo-feng Zhang (Department of Mathematics, Lanzhou University, Lanzhou 730000, China) 

作者机构：Department of Mathematics Lanzhou University Lanzhou 730000 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2003年第21卷第3期

页      面：375-382页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：Neutral delay differential equations (A,B,C)-method RK method Parallel diagonally-implicit iteration RK method. 

摘      要：Consider the following neutral delay-differential equations with multiple delays (NMDDE) where γ 0, L, Mj and Nj 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 methods. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1).