Numerical simulation of a nonlinear system of space-fractional Klein-Gordon-Zakharov equations using the Fourier spectral method

Document Type : Research Paper

Authors

1 Department of Mathematics, Ahvaz branch, Islamic Azad University, Ahvaz, Iran.

2 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

3 Department of Mathematics, Osku Branch, Islamic Azad University, Osku, Iran.

Abstract

An accurate and efficient numerical approach for the nonlinear space-fractional Klein-Gordon-Zakharov (KGZ) system of equations incorporating the fractional Laplacian operator is proposed in this study. The method is designed to preserve both mass and energy, which is crucial for accurately solving such complex systems. The spatial discretization is carried out using the Fourier spectral method. In contrast, temporal discretization is achieved through the fourth-order exponential time-differencing Runge-Kutta (ETDRK4) technique, ensuring both efficiency and stability. We prove the convergence of the proposed method, establishing a theoretical foundation for its application. To assess the efficiency and versatility of the proposed method, we report on a series of numerical simulations. The outcomes of these simulations are displayed in tables and graphs, illustrating the performance of the method regarding the approximation error, convergence order, and execution time for various fractional values.

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Main Subjects

References

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Computational Methods for Differential Equations
Volume 14, Issue 1
January 2026
Pages 188-200

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History

  • Receive Date: 16 December 2024
  • Revise Date: 09 February 2025
  • Accept Date: 03 March 2025

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