A numerical method based on probability theory

来源期刊：中南大学学报(英文版)2003年第2期

论文作者：唐立 邹捷中 杨文胜

文章页码：159 - 161

Key words：probabilistic method; Brownian family with drift; finite element spaces over boundaries

Abstract: By using the connections between Brownian family with drift and elliptic differential equations, an efficient probabilistic computing method is given. This method is applied to a wide-range Dirichlet problem. Detail ana-lysis and deduction of solving the problem are offered. The stochastic representation of the solution to the problem makes a 3-dimensional problem turned into a 2-dimensional problem. And an auxiliary ball is constructed. The strong Markov property and the joint distributions of the time and place of hitting spheres for Brownian family with drift are employed. Finally, good convergence of the numerical solution to the problem over domain with arbitrary boundary is obtained.