高维Dirichlet问题数值解的概率方法(英文)  

Probabilistic Methods for Numerical Solutions to Higher-Dimensional Dirichlet Problems

作　　者：唐立[1] 黄立宏[1] 杨文胜[2] 

机构地区：[1]湖南大学数学与计量经济学院,长沙410082 [2]中南大学铁道校区数学学院,长沙410075

出　　处：《应用概率统计》2007年第3期231-237,共7页Chinese Journal of Applied Probability and Statistics

基　　金：This research was supported by National Natural science Foundation Of China(19871027).

摘　　要：本文用概率方法求得高维Dirichlet内问题和外问题在一般区域上的数值解.高维漂移布朗族对停时具有强马氏性,它在球面上的击中时和位置分布已知,再利用Dirichlet问题解的随机表达式,我们可以获得高维Dirichlet问题的数值解.In this paper, numerical solutions to the higher-dimensional Dirichlet interior problems and exterior problems over ordinary domains by probabilistic methods are obtained. Higher- dimensional Brownian family with drift has the strong Markov property and its distributions of the time and place of hitting spheres are known. By these and the stochastic representations of the solution we get the numerical solutions to the higher-dimensional Dirichlet problems.

关 键 词：高维Dirichlet 概率方法 漂移布朗族 

分 类 号：O211[理学—概率论与数理统计] O241[理学—数学]