随机微分方程平衡θ-Heun方法的稳定性  

Stability of balancedθ-Heun method for stochastic differential equations

作　　者：康红喜 张引娣[1] 蒋茜 KANG Hongxi;ZHANG Yindi;JIANG Qian(School of Science, Chang’an University, Xi’an 710064, China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《合肥工业大学学报（自然科学版）》2021年第2期284-288,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11572146)。

摘　　要：求解随机微分方程时,为了更好地使数值解逼近解析解,文章将平衡法与θ-Heun法结合构成平衡θ-Heun法。当控制参数确定时,对于带有乘性噪音的随机微分方程,给出了平衡θ-Heun法均方稳定的条件,并证明了平衡θ-Heun法的指数稳定性。最后的数值算例给出了相关结论的验证,比较了3种Heun方法的稳定性。When solving stochastic differential equations,in order to better approximate the numerical solution to the analytical solution,the balancedθ-Heun method was obtained by combining the balance method andθ-Heun method.For a stochastic differential equation with multiplicative noise,as the control parameters were determined,the conditions of the mean square stability for the balancedθ-Heun method were given and the exponential stability of the balancedθ-Heun method was proved.Finally,the numerical example was given to verify theoretical results and the stability of three Heun methods was compared.

关 键 词：随机微分方程 平衡θ-Heun法 均方稳定性 指数稳定性 

分 类 号：O211.63[理学—概率论与数理统计]