向前型分段连续微分方程的数值解(英文)  

Numerical Solutions of Differential Equations with Piecewise Constant Arguments of Advanced Type

作　　者：王琦[1] 温洁嫦[1] 

机构地区：[1]广东工业大学应用数学学院,广东广州510006

出　　处：《应用数学》2011年第4期712-717,共6页Mathematica Applicata

基　　金：the National Natural Science Foundation of China(51008084)

摘　　要：本文讨论了向前型分段连续微分方程Euler-Maclaurin方法的收敛性和稳定性,给出了Euler-Maclaurin方法的稳定条件,证明了方法的收敛阶是2n+2,并且得到了数值解稳定区域包含解析解稳定区域的条件,最后给出了一些数值例子用以验证本文结论的正确性.This paper is concerned with the convergence and the stability of Euler-Maclaurin methods for solutions of differential equations with piecewise constant arguments of advanced type.The conditions of stability for the Euler-Maclaurin methods are given.It is proved that the order of convergence is 2n＋2.And the conditions under which the numerical stability region contains the analytic stability region are obtained.Finally,several numerical examples are given to demonstrate our main results.

关 键 词：收敛性 稳定性 Euler-Maclaurin方法 分段连续项 

分 类 号：O241.81[理学—计算数学]