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Yayın Numerical approximation of dirichlet problem in bounded domains and applications(Maltepe Üniversitesi, 2009) Rachieru, OanaWe consider numerical approximation of Dirichlet problem for the Laplace equation in a domain D ? R d , that is we will consider the problem of finding a C 2 function. Using probabilistic methods we can give explicit reprezentation of solution of Dirichlet problem u(z) = E z f(B?D ) , where Bt is a Brownian motion starting at B0 = z, E z denotes the expectation of function in B?D , and ?D = inf{t ? 0, Bt ?/ D} is the exit time of Brownian motion from D. We give a Mathematical implementation of function u(z) for different choices of f and domain D (half-plane, unit disc, rectangle, triangle) and we apply it to obtain some numerical results.
