Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral Method

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan, Iran.

Abstract

This paper presents a numerical scheme for solving the non-linear time fractional Klein-Gordon equation. To approximate spatial derivatives, we employ the pseudo-spectral method based on Lagrange polynomials at Chebyshev points, while using the finite difference method for time discretization. Our analysis demonstrates that this scheme is unconditionally stable, with a time convergence order of $\mathcal{O}({3-\alpha})$. Additionally, we provide numerical results in one, two, and three dimensions, highlighting the high accuracy of our approach. The significance of our proposed method lies in its ability to efficiently and accurately address the non-linear time fractional Klein-Gordon equation. Furthermore, our numerical outcomes validate the effectiveness of this scheme across different dimensions.

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Main Subjects



Articles in Press, Accepted Manuscript
Available Online from 08 July 2024
  • Receive Date: 25 October 2023
  • Revise Date: 29 May 2024
  • Accept Date: 25 June 2024