The Numerical Solution of Klein-Gorden Equation by Using Nonstandard Finite Difference
الموضوعات : فصلنامه ریاضیHoda 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
الکلمات المفتاحية: Klein-Gorden equation, Nonstandard finite difference, Three level explicit,
ملخص المقالة :
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.
