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

Subject Areas : International Journal of Mathematical Modelling & Computations

Hoda Shekarabi ¹ , Jalil Rashidinia ²

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

Received: 2019-03-15 Accepted : 2019-08-14 Published : 2019-09-30

Keywords: Klein-Gorden equation, ‎Nonstandard finite difference, ‎Three level explicit‎,

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 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.