The pseudo-spectral method based on the reproducing kernel Hilbert spaces for solving the nonlinear Klein-Gordon problem

Document Type : Research Article

Authors

1 Postdoc Researcher, Department of Computer Sciences, Faculty of Mathematics, Shahid Beheshti University

2 Professor, Department of Computer Sciences, Faculty of Mathematics, Shahid Beheshti University

Abstract

In this paper, a pseudo-spectral method based on the reproducing kernels of Hilbert spaces will be introduced to solve the nonlinear Klein-Gordon problem. In order to approximate the spatial derivatives of the problem, we use the operational matrices obtained by the reproducing kernels of Hilbert spaces and also a fourth order Runge-Kutta method is used to discretize the time domain. Using reproducing kernel Hilbert space operational matrices and enforce the basis functions to satisfy the boundary conditions exactly are the main advantages of the proposed method. Several examples are presented to illustrate the efficiency and ability of the method for solving nonlinear time dependent problems.

Keywords

Files

Share

How to cite

Statistics