解随机森林发展方程的半隐式欧拉法的收敛性(英文)  

Convergence of the semi-implicit Euler method for stochastic forest evolution equations

作　　者：丁效华[1] 马强[1] 

机构地区：[1]哈尔滨工业大学(威海)数学系

出　　处：《黑龙江大学自然科学学报》2008年第6期719-730,共12页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(10671047);the Project of Science Research Foundation(HITC 200713)

摘　　要：一般来说,大多数随机偏微分方程并不存在显式解,因此,数值方法是研究这类方程解的性质的十分有效的工具。应用半隐式欧拉方法求解一类随机森林发展方程,从而得到其近似解,并证明了当满足一些比线性增长条件和全局利普希茨条件弱的条件时,半隐式欧拉格式将依概率收敛于方程的解析解,其收敛阶为p=12.In order to approximate the solutions of a class of stochastic forest evolution equations, a numerical method will be given. In general, the explicit solutions of most of stochastic partial differential equations do not exist, so numerical methods are invaluable tools for us to explore their properties. This paper is to show that under some conditions which are weaker than linear growth condition and global Lipschitz condition, the semi - implicit Euler scheme converges to the analytic solutions of the stochastic forest evolution equations in probability. Then we get the order of convergene p=1/2.

关 键 词：随机森林发展方程 半隐式欧拉方法 依概率收敛 李雅普偌夫函数 

分 类 号：O241.8[理学—计算数学]