BENTATA, FATIMA EZAHRA2020-10-272020-10-272020http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/20083We consider the Laplace equation, with different boundary conditions, on a planar domain defined as a disc with a small perturbation of its boundary. First, we find an asymptotic solution in the interior of the disc using two analytical methods: separations of variables and Laplace’s formula. A third approach consists in combining the asymptotic approach with finited ifferences in polar coordinates. Some numerical examples are given at the end of this work.enLaplace’s equation, separation of variable, Poisson’s formula, finite difference in polar coordinates, perturbed domainsThesis