利用映射技术构造随机微分方程保守恒量数值方法(英文)  

Conserved-quantity-preserving method for stochastic differential equations by projection technique

作　　者：丁效华[1] 李绪亮 王振宇 DING Xiaohua;LI Xuliang;WANG Zhenyu(Department of Mathematics,Harbin Institute of Technology at Weihai,Weihai 264209,China;Department of Mathematics,Qingdao University,Qingdao 266071,China)

机构地区：[1]哈尔滨工业大学(威海)数学系,威海264209 [2]青岛大学数学系,青岛266071

出　　处：《黑龙江大学自然科学学报》2018年第5期505-515,共11页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Key R&D Program of China(2017YFC1405600);the National Natural Science Foundation of China(11271101;11501150)

摘　　要：利用映射技术给出一类求解随机微分方程的保守恒量数值方法。利用任意两个数值方法确定映射方向,将原始方法所得数值解沿着给定方向映射到方程守恒量所确定的流形上;证明所构造的数值方法与原始方法具有相同的均方收敛阶。数值实例验证了所构造映射方法的有效性。A class of conserved-quantity-preserving numerical methods for stochastic differential equations are constructed by projection technique. Specifically,a projection direction determined by two numerical methods is employed,then the numerical solution of conserved-quantity-preserving numerical method is projected onto the manifold determined by the conserved quantity along the projection direction. These methods are proved to share the mean-square convergence order of their underlying methods. Numerical experiments are implemented to show the validity of the projection methods.

关 键 词：随机微分方程 数值方法 守恒量 均方收敛 映射技术 

分 类 号：O241.8[理学—计算数学]