椭圆型方程Dirichlet问题的概率数值解法

Probabilistic Numerical Solution for Dirichlet Problem of Elliptic Equations

在文献[1]和[2]中,已经给出Schro dinger方程和一类抛物型方程的概率数值解法。本文将此概率数值方法推广到求解一类非常一般的椭园型方程。其思想是使用关于Brown运动的随机微分方程表示椭园方程解的随机表达式中出现的Markov过程。

In [1] and [2], a probabilistic numerical solution was given for schrodinger equation and a class of parabolic equation. In this paper, the probabilistic numerical method is genaralized to solve a class of very general elliptic equations, The idea is to use the stochastic differential equation with respect to Brownian motion to represent the Markov process which appear in the stochastic representation of the solution of the elliptic equation.