Quasi Interpolation of radial basis functions-pseudospectral method for solving nonlinear Klein–Gordon and sine-Gordon equations

We propose a new approach for solving nonlinear Klein–Gordon and sine-Gordon equations based on radial basis function-pseudospectral method (RBF-PS). The proposed numerical method is based on quasiinterpolation of radial basis function differentiation matrices for the discretization of spatial derivatives combined with Runge–Kutta time stepping method in order to deal with the temporal part of the problem. The method does not require any linearization technique; in addition, a new technique is introduced to force approximations to satisfy exactly the boundary conditions. The introduced scheme is tested for a number of one- and two-dimensional nonlinear problems. Numerical results and comparisons with reported results in the literature are given to validate the presented method, and the reported results show the applicability and versatility of the proposed method.