Rosenbrock方法求解多延时微分方程组的GP_mL-稳定性（英文）  

GP_mL-stability of the Rosenbrock methods for the systems of differential equations with many delays

作　　者：陆志雯[1] 

机构地区：[1]上海理工大学理学院

出　　处：《上海师范大学学报（自然科学版）》2014年第2期111-116,共6页Journal of Shanghai Normal University(Natural Sciences)

摘　　要：研究了用Rosenbrock方法求解多延时微分方程组数值解的稳定性.Rosenbrock方法是求解刚性常微分方程的有效方法,基于Lagrange插值,借助于理论解渐近稳定的条件,对于线型方程组模型,分析了Rosenbrock方法的GPmL-稳定性,并证明了用Rosenbrock方法数值求解多延时微分方程组是GPmL-稳定的当且仅当它是L-稳定的.This paper deals with the stability analysis of the Rosenbrock methods for the numerical solutions of the systems of differential equations with many delays. The GPmL-stability behavior of the Rosenbrock methods is analyzed for the solutions of linear test equations. We show that the Rosenbrock methods are GPmL-stable if and only if they are L-stable.

关 键 词：延时微分方程组 GPmL-稳定性 ROSENBROCK方法 

分 类 号：O241.8[理学—计算数学]