Ӧ�ø���ͳ�� 2007, 23(3) 231-237 DOI:      ISSN: 1001-4268 CN: 31-1256

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Probabilistic Methods for Numerical Solutions to Higher-Dimensional Dirichlet Problems
Tang Li, Huang Lihong, Yang Wensheng
College of Mathematics and Econometrics, Hunan University; School of Mathematics, Railway Campus, Central South University
Abstract: 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.
Keywords: Higher-dimensional Dirichlet problem   probabilistic method   Brownian family with drift.  
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