非线性比例尺微分方程组的稳定性分析及数值处理(英文)  

Analysis and numerical treatment for nonlinear systems of pantograph equations with many delays

作　　者：单恺婷[1] 江峰[1] 匡蛟勋[1] 田红炯[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2009年第2期111-117,共7页Journal of Shanghai Normal University(Natural Sciences)

基　　金：Supported in part by the NSF of China(10171067).

摘　　要：主要研究了多延时非线性比例尺方程理论解及数值解的稳定性质y′(t)=f(t,y(t),y(λ1t),…,y(λdt)),其中f:×N×…×N→N,y:→N,0<λd<…<λ1<1.获得了比例尺微分方程稳定及渐近稳定的充分条件,同时研究了隐式欧拉方法的稳定性质.This paper deals with the stability properties of the analytic and numerical solutions of nonlinear systems of pantograph differential equations with many delays. Sufficient conditions for the trivial solutions of the pantograph differential equations to be stable and asymptotically stable are derived. We also focus on the corresponding numerical stability properties of the implicit Euler method solving the underlying differential equation.

关 键 词：比例尺微分方程 稳定性 时滞微分方程 

分 类 号：O241.8[理学—计算数学]