Solution of Klein-Gordon Equation by a Method of Lines Using Reproducing Kernel Hilbert Space Method

Abstract

This paper presents a method of lines solution based on the reproducing kernel Hilbert space method to the nonlinear one-dimensional Klein-Gordon equation that arises in many scientific fields areas. Our method uses discretization of the partial derivatives of the space variable to get a system of ODEs in the time variable and then solve the system of ODEs using reproducing kernel Hilbert space method. Consider two examples to validate the proposed method. Compare the results with the exact solution by calculating the error norms $L_2$ and $L_∞$ at various time levels. The results show that the presented scheme is a systematic, effective and powerful technique for the solution of Klein-Gordon equation.