On convergence of the method of fundamental solutions for solving the Dirichlet problem of Poisson’s equation

In this paper the convergence of using the method of fundamental solutions for solving the boundary value problem of Laplace’s equation in R2 is established, where the boundaries of the domain and fictitious domain are assumed to be concentric circles. Fourier series is then used to find the particular solutions of Poisson’s equation, which the derivatives of particular solutions are estimated under the L2 norm. The convergent order of solving the Dirichlet problem of Poisson’s equation by the method of particular solution and method of fundamental solution is derived.