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

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

作者机构：School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China 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 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2009年第25卷第4期

页      面：607-616页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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) 

主　　题：Delay differential equations delay-dependent stability asymptotic stability ^-（O）-stability linearmultistep methods general linear methods 

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.