Delay-dependent Stability Analysis of Multistep Methods for Delay Differential Equations  

作　　者：Cheng-ming Huang Yang-zi Hu Hong-jiong Tian 

机构地区：[1]School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China [2]Department of Mathematics, Shanghai Normal University, Division of Computational Science, E-Institute of Shanghai Universities, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第4期607-616,共10页应用数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.10671078);the Program for New Century Excellent Talents in University,the State Education Ministry of China. supported in part by E-Institutes of Shanghai Municipal Education Commission (No.E03004);National Natural Science Foundation of China(No.10671130);Shanghai Science and Technology Commission(No.06JC14092);Shuguang Project of Shanghai Municipal Education Commission(No.06SG45);the Shanghai Leading Academic Discipline Project(No.S30405)

摘　　要：This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of r（0）-stable methods are found. Later, some examples of r（0）-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results.This paper deals with the delay-dependent stability of numerical methods for delay differential equations. First, a stability criterion of Runge-Kutta methods is extended to the case of general linear methods. Then, linear multistep methods are considered and a class of r（0）-stable methods are found. Later, some examples of r（0）-stable multistep multistage methods are given. Finally, numerical experiments are presented to confirm the theoretical results.

关 键 词：Delay differential equations delay-dependent stability asymptotic stability ^-（O）-stability linearmultistep methods general linear methods 

分 类 号：O172.1[理学—数学]