The Numerical Solution of Klein-Gorden Equation by Using Nonstandard Finite Difference

Document Type : Full Length Article


School of Mathematics‎, ‎Iran University of Science and Technology‎, ‎Narmak‎, ‎Tehran 1684613114‎, ‎Iran


‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed method when applied to one dimensional nonlinear Klein-Gorden equation‎, ‎is unconditionally stable‎. ‎We illustrate the usefulness of the proposed method by applying it on two examples.