A numerical method based on probability theory
唐立, 邹捷中, 杨文胜 · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2003
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 Diriehlet problem. Detail analysis 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.