Stability of linear multistep methods for delay differential equations in the light of Kreiss resolvent condition  

作　　者：赵景军 刘明珠 

出　　处：《Journal of Harbin Institute of Technology(New Series)》2001年第2期155-158,共4页哈尔滨工业大学学报（英文版）

基　　金：&&

摘　　要：This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.

关 键 词：Delay differential equations linear multistep methods resolvent condition 

分 类 号：O241[理学—计算数学]