摘要
为了提高求解随机微分方程数值方法的稳定性,对Heun方法进行改进得到θ-Heun方法。对于带有乘性噪声的随机微分方程,得到了θ-Heun方法均方稳定和指数稳定的充要条件,且证明了θ-Heun方法中这两种稳定性是等价的。用数值例子验证了θ-Heun方法的稳定性比Heun方法好。
In order to improve the stability of the numerical method for solving stochastic differential equation,the θ-Heun method was obtained by improving the Heun method. For a stochastic differential equation with multiplicative noise,the sufficient and necessary conditions of the mean square stability and the exponential stability for the θ-Heun method were obtained. The two stability of the θ-Heun method were proved to be equivalent. Finallly,it is proved that the stability of the θ-Heun method was better than that of Heun method by numerical example.
出处
《河南科技大学学报（自然科学版）》
CAS
北大核心
2018年第4期84-87,93,共5页
Journal of Henan University of Science And Technology:Natural Science
基金
国家自然科学基金项目(211012140334
11401044
11471005)
关键词
随机微分方程
θ-Heun方法
均方稳定
指数稳定
随机变量
均方稳定函数
stochastic differential equations
θ-Heun method
mean square stability
exponential stability
random variable
mean square stability function
作者简介
李瑞(1992-),女,陕西榆林人,硕士生.;张引娣(1962-),女,陕西三原人,教授,博士,硕士生导师,主要研究方向为微分方程数值方法.
