CAJ | 학술논문

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.
본문용개솔방법구득고유Dirichlet내문제화외문제재일반구역상적수치해.고유표이포랑족대정시구유강마씨성,타재구면상적격중시화위치분포이지,재이용Dirichlet문제해적수궤표체식,아문가이획득고유Dirichlet문제적수치해.
In this paper, numerical solutions to the higher-dimensional Dirichlet interior problems and exterior problems over ordinary domains by probabilistic methods are obtained. Higherdimensional 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.