两步Runge-Kutta法求解延迟微分方程的GPL_m-稳定性(英文)  

GPL_m-stability of Two-Step Runge-Kutta Methods for Delay Differential Equations

作　　者：丛玉豪[1] 蒋成香[2] 

机构地区：[1]上海师范大学数学系,上海200234 [2]上海师范大学天华学院,上海201815

出　　处：《系统仿真学报》2011年第7期1366-1368,共3页Journal of System Simulation

基　　金：The National Natural Science Foundation(10971140)

摘　　要：讨论了两步Runge-Kutta方法求解延迟微分方程的数值稳定性,分析了求解线性试验方程的两步Runge-Kutta方法的稳定性态。证明了两步Runge-Kutta方法是GPLm-稳定的,当且仅当它求解常微分方程是L-稳定的。The stability of two-step Runge-Kutta methods for delay differential equations（DDEs） with many delays was dealt with,and the stability for the test equation was analyzed.It is shown that a two-step Runge-Kutta method is GPLm-stable if and only if the corresponding method for ordinary differential equation is L-stable.

关 键 词：延迟微分方程 两步Runge-Kutta方法 GPL-稳定性 L-稳定性 

分 类 号：O241.8[理学—计算数学]