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

Abstract

We provide a numerical method in this study to solve the one dimensional nonlinear Klein-Gorden problem. We provide a detailed description of the mathematical formulation process. The technique is based on nonstandard finite differences and is explicit at three levels. The step sizes' denominator function is nonlinear. We have provided a stability study of the approach and shown its unconditional stability when applied to the one dimensional nonlinear Klein-Gorden problem. We use the suggested strategy to two cases to demonstrate its utility.