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Two Fibonacci operational matrix pseudo-spectral schemes for nonlinear fractional Klein–Gordon equation

Author

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  • Y. H. Youssri

    (Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt)

Abstract

This paper is devoted to developing spectral solutions for the nonlinear fractional Klein–Gordon equation. The typical collocation method and the tau method are employed for obtaining the desired numerical solutions. In order to do this, a new operational matrix of fractional derivatives of Fibonacci polynomials is established. The idea behind the derivation of this matrix is based on utilizing the connection formula between the Fibonacci and Chebyshev polynomials. The introduced operational matrix is used along with the weighted residual quadrature spectral method and the collocation method to convert the nonlinear fractional Klein–Gordon equation into a system of algebraic equations. By solving the resulting system, we obtain a semi-analytic solution. The convergence and error analysis of the method are discussed. Some numerical results and discussions are presented aiming to illustrate the wide applicability and accuracy of the proposed algorithms.

Suggested Citation

  • Y. H. Youssri, 2022. "Two Fibonacci operational matrix pseudo-spectral schemes for nonlinear fractional Klein–Gordon equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-19, April.
    • Handle: RePEc:wsi:ijmpcx:v:33:y:2022:i:04:n:s0129183122500498
    DOI: 10.1142/S0129183122500498
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    Cited by:

    1. Taghipour, M. & Aminikhah, H., 2022. "A spectral collocation method based on fractional Pell functions for solving time–fractional Black–Scholes option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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