Pathwise approximation of random ordinary differential equations

被引：31

作者：

Grüne, L ^{[1
]}

Kloeden, PE ^{[1
]}

机构：

[1] Univ Frankfurt, Fachbereich Math, D-60054 Frankfurt, Germany

来源：

BIT | 2001年 / 41卷 / 04期

关键词：

random ordinary differential equation; Euler scheme; Henn scheme; time averaging;

D O I：

10.1023/A:1021995918864

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Standard error estimates for one-step numerical schemes for nonautonomous ordinary differential equations usually assume appropriate smoothness in both time and state variables and thus are not suitable for the pathwise approximation of random ordinary differential equations which are typically at most continuous or Holder continuous in the time variable. Here it is shown that the usual higher order of convergence can be retained if one first averages the time dependence over each discretization subinterval.

引用

页码：711 / 721

页数：11