The MFS as a basis for the PIM or the HAM – comparison of numerical methods

The aim of this paper is to present implementation of the Method of Fundamental Solutions. Using the MFS the fundamental solution of the operators appearing in the governing equations should be known. For many engineering problems the governing equations are linear with unknown fundamental solutions or nonlinear. The purpose of this paper is implementation of the Picard Iterations Method or Homotopy Analysis Method in such case. Both methods are supported by the MFS. Some engineering problems described by linear equation with unknown fundamental solution and system of nonlinear equations are considered. The numerical experiment, solving these engineering problems, is performed using both methods. The correctness of the results obtained by both methods is checked. The conditions of the convergence of both methods are described.