求解随机微分方程的θ-Heun方法的收敛性  

The Convergence ofθ-Heun Method for Solving Stochastic Differential Equations

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作  者:张引娣[1] 李瑞 刘奋进 ZHANG Yindi;LI Rui;LIU Fenjin(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》2019年第1期34-38,共5页Journal of Zhengzhou University:Natural Science Edition

基  金:国家自然科学基金项目(211012140334,11401044,11471005).

摘  要:Heun方法是一种求解随机微分方程数值解的重要方法,在该方法的基础上构造出一种新的数值求解方法,即θ-Heun方法,且研究了θ-Heun方法用于求解随机微分方程的收敛性.针对一个具体的标量自治随机微分方程,当方程的两个系数都满足Lipschitz和线性增长条件时,得到θ-Heun方法在均值意义、均方意义上的局部收敛阶分别为2和1,均方强收敛阶为1.并通过数值实例证明该方法比Heun方法得到的数值解更逼近解析解.Heun method was an important numerical technique for solving stochastic differential equations.A new method based on Heun method was developed,known as theθ-Heun method.And the convergence of this method was examined.For scalar autonomous stochastic differential equations,when the two coefficients satisfied the linear growth condition and global Lipschitz condition,the order of its local convergence in mean was two,the order of its local convergence in mean square was one,and the order of its strong convergence square was one.Finally,the numerical solution obtained byθ-Heun method was more approximate to analytical solution than Heun method,which was proved by numerical example.

关 键 词:随机微分方程 θ-Heun方法 收敛性 LIPSCHITZ条件 

分 类 号:O211.63[理学—概率论与数理统计;理学—数学]

 

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