边值问题的概率数值方法  

Probabilistic Numerical Method for Boundary Value Problems

作　　者：唐立[1] 杨文胜[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075

出　　处：《数学物理学报（A辑）》2008年第1期81-85,共5页Acta Mathematica Scientia

基　　金：国家自然科学基金(19871027);湖南省高校青年骨干教师基金资助

摘　　要：该文运用概率理论研究了一种有界和无界区域上边值问题的数值方法.其主要思想如下:先写出所求边值问题解的随机表达方式,再构造一个辅助球,并且通过区域边界上的剖分将问题离散化,最后利用漂移布朗族的强马尔可夫性和它的球面首中时、首中位置的分布,获得离散问题的解.In this paper a kind of numerical method for boundary value problems over bounded or unbounded domains is investigated by probability theory. It＇s main idea is as follows： Firstly, represent the solution of the boundary value problem as the stochastic representations. Secondly, construct an auxiliary ball and subdivide the boundaries of the domains to make the problem discretized. Finally, by using the strong Markov property and the distributions of the time and place of hitting spheres for Brownian motion with drift, obtain the solutions to the discretized problems.

关 键 词：概率数值方法 边值问题 漂移布朗运动 

分 类 号：O211.9[理学—概率论与数理统计] O241.82[理学—数学]