随机常微分方程的龙格库塔解法(英文)  

Runge-Kutta approximations for stochastic ordinary differential equations

作　　者：胡建成[1] 罗敏[1] 

机构地区：[1]成都信息工程学院数学学院,成都610225

出　　处：《四川大学学报（自然科学版）》2012年第4期747-752,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：成都信息工程学院校选科研项目(CRF200904)

摘　　要：本文讨论了随机Runge-Kutta格式的构造.基于比较完善的确定性常微分方程数值求解法,随机Runge-Kutta格式也可以通过随机Taylor展式得到.文中讨论了一阶,二阶和一般两步二阶随机Runge-Kutta格式.通过对一个线性随机微分方程和一个二阶非线性随机微分方程的数值模拟表明,随机Runge-Kutta法是一种求解随机微分方程的有效方法.This paper discusses the construction of stochastic Runge-Kutta schemes. Based on well-es- tablished numerical methods for deterministic ordinary differential equations, the stochastic Runge-Kut- ta type methods can be obtained by comparing the stochastic Taylor expansion. One order, second order and general two-stage second order Runge-Kutta schemes are presented. A linear stochastic differential equation and a second-order nonlinear stochastic differential equation are simulated. Numerical results demonstrate that stochastic Runge-Kutta method is an effective method for solving stochastic differential equations.

关 键 词：随机微分方程 WIENER过程 随机Taylor展式 随机Runge-Kutta法 

分 类 号：O241.82[理学—计算数学]