随机微分方程平衡θ-Heun法的收敛性  

Convergence 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(Faculty 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：《郑州大学学报（理学版）》2020年第4期89-95,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(11572146)。

摘　　要：对θ-Heun方法改进得到平衡θ-Heun方法,研究该方法用于求解随机微分方程的收敛性。对于系数都满足Lipschitz和线性增长条件的标量自治随机微分方程,证明了平衡θ-Heun方法在均值意义上、均方意义上的局部收敛阶分别为3/2、1,均方强收敛阶为1/2。通过数值实验验证了平衡θ-Heun方法的收敛性,并用数值算例说明了该方法得到的数值解与解析解逼近程度优于θ-Heun方法。The balancedθ-Heun method was obtained by improving theθ-Heun method.And the convergence of this method to solve the stochastic differential equation was studied.For the scalar autonomous stochastic differential equation with all coefficients satisfied the conditions of Lipschitz and linear growth,it was proved that the local convergence orders of the balancedθ-Heun method were 3/2 and 1 in the sense of mean value and mean square,respectively;and its strong convergence order was 1/2.At last,the convergence of the method was verified by numerical experiments.And a numerical example was given to illustrate that the numerical solution of the stochastic differential equation obtained by the balancedθ-Heun method was more approximate to the analytical solution.

关 键 词：平衡θ-Heun方法 随机微分方程 收敛阶 LIPSCHITZ条件 线性增长条件 

分 类 号：O211.63[理学—概率论与数理统计]