The numerical solution of Klein-Gorden equation by using Nonstandard Finite Difference

Document Type: Review Article

Authors

1 aSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran.

2 IUST and IAUCTB

Abstract

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 nite di erence.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.

Keywords