随机微分方程θ-Heun方法的稳定性  

Stability of θ-Heun Method for Stochastic Differential Equations

作　　者：李瑞 张引娣[1] 刘奋进 

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《河南科技大学学报（自然科学版）》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)

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.

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 

分 类 号：O175[理学—数学]