NUMERICAL SOLUTION FOR TWO-DIMENSIONAL NONLINEAR KLEIN-GORDON EQUATION THROUGH MESHLESS SINGULAR BOUNDARY METHOD

Abstract

In this study, the singular boundary method (SBM) is employed for the simulation of nonlinear Klein-Gordon equation with initial and Dirichlet-type boundary conditions. The θ-weighted and Houbolt finite difference method is used to discretize the time derivatives. Then the original equations are split into a system of partial differential equations. A splitting scheme is applied to split the solution of the inhomogeneous governing equation into homogeneous solution and particular solution. To solve this system, the method of particular solution in combination with the singular boundary method is used for particular solution and homogeneous solution, respectively. Finally, several numerical examples are provided and compared with the exact analytical solutions to show the accuracy and efficiency of method in comparison with other existing methods.