Stability Analysis of Runge-Kutta Methods for Nonlinear Neutral Volterra Delay-Integro-Differential Equations  

作　　者：Wansheng Wang Dongfang Li 

机构地区：[1]School of Mathematics and Computational Sciences,Changsha University of Science&Technology,Yuntang Campus,Changsha 410114,China [2]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2011年第4期537-561,共25页高等学校计算数学学报（英文版）

基　　金：supported by NSF of China(Grant No.11001033);Natural Science Foundation of Hunan Province(Grant No.10JJ4003);Chinese Society for Electrical Engineering,and Graduates’innovation fund of HUST(No.HF-08-02-2011-011).

摘　　要：This paper is concerned with the numerical stability of implicit Runge-Kutta methods for nonlinear neutral Volterra delay-integro-differential equations with constant delay.Using a Halanay inequality generalized by Liz and Trofimchuk,we give two sufficient conditions for the stability of the true solution to this class of equations.Runge-Kutta methods with compound quadrature rule are considered.Nonlinear stability conditions for the proposed methods are derived.As an illustration of the application of these investigations,the asymptotic stability of the presented methods for Volterra delay-integro-differential equations are proved under some weaker conditions than those in the literature.An extension of the stability results to such equations with weakly singular kernel is also discussed.

关 键 词：Neutral differential equations Volterra delay-integro-differential equations Runge-Kutta methods stability 

分 类 号：O17[理学—数学]