Approximate analytic solution of Dirichlet’s problems for Laplace’s equation in planar domains by a perturbation method

In this paper we propose a regular perturbation method to obtain approximate analytic solutions of exterior and interior Dirichlet’s problems for Laplace’s equation in planar domains. This method, starting from a geometrical perturbation of these planar domains, reduces our problems to a family of classical Dirichlet’s problems for Laplace’s equation in a circle. Numerical examples are given and comparisons are made with the solutions obtained by other approximation methods.