Rachieru, Oana2024-07-122024-07-122009Rachieru, O. (2009). Numerical approximation of dirichlet problem in bounded domains and applications. Maltepe Üniversitesi. s. 310.9.78605E+12https://hdl.handle.net/20.500.12415/2910We 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.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessConference Object311310