随机微分方程Runge-Kutta方法的矩指数稳定及矩渐近稳定性

J4 ›› 2012, Vol. 50 ›› Issue (01): 67-68.

随机微分方程Runge-Kutta方法的矩指数稳定及矩渐近稳定性

张雨馨^1,2

1. 吉林大学数学学院, 长春 130012|
2. 哈尔滨工程大学理学院, 哈尔滨 150001

收稿日期:2011-12-06 出版日期:2012-01-26 发布日期:2012-03-06
通讯作者: 张雨馨 E-mail:xyz.jl@163.com

Moment Exponential and Moment Asymptotic Stabilities ofRunge-Kutta Methods for Stochastic Differential Equations

ZHANG Yuxin^1,2

1. College of Mathematics, Jilin University, Changchun 130012, China;
2. College of Science, Harbin Engineering University, Harbin 150001, China

Received:2011-12-06 Online:2012-01-26 Published:2012-03-06
Contact: ZHANG Yuxin E-mail:xyz.jl@163.com

摘要/Abstract

摘要：

考虑逼近随机微分方程的1.5阶Runge-Kutta法的矩指数稳定性和矩渐近稳定性, 对于标量线性检验方程, 证明了随机Runge-Kutta法的矩指数稳
定性和矩渐近稳定性是一致的, 并给出了这两种稳定性的存在条件.

关键词: Runge-Kutta方法, 矩指数稳定, 矩渐近稳定

Abstract:

Moment exponentical and moment asymptotic stabilities of RungeKutta method with strong order 15 for stochastic differential equations
was studied. We have proved that for scalar linear test equations, these stabilities of RungeKutta method are equivalent and we gave the conditions for these stabilities existing.

Key words: RungeKutta method, moment exponential stability, moment asymptotical stability

中图分类号:

O211.63

张雨馨. 随机微分方程Runge-Kutta方法的矩指数稳定及矩渐近稳定性[J]. J4, 2012, 50(01): 67-68.

ZHANG Yuxin. Moment Exponential and Moment Asymptotic Stabilities ofRunge-Kutta Methods for Stochastic Differential Equations[J]. J4, 2012, 50(01): 67-68.

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