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A Highly Accurate Computational Approach to Solving the Diffusion Equation of a Fractional Order

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  • Haifa Bin Jebreen

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

This study aims to present and apply an effective algorithm for solving the TFDE (Time-Fractional Diffusion Equation). The Chebyshev cardinal polynomials and the operational matrix for fractional derivatives based on these bases are relied on as crucial tools to achieve this objective. By employing the pseudospectral method, the equation is transformed into an algebraic linear system. Consequently, solving this system using the GMRES method (Generalized Minimal Residual) results in obtaining the solution to the TFDE. The results obtained are very accurate, and in certain instances, the exact solution is achieved. By solving some numerical examples, the proposed method is shown to be effective and yield superior outcomes compared to existing methods for addressing this problem.

Suggested Citation

  • Haifa Bin Jebreen, 2024. "A Highly Accurate Computational Approach to Solving the Diffusion Equation of a Fractional Order," Mathematics, MDPI, vol. 12(13), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1965-:d:1421525
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    References listed on IDEAS

    as
    1. A. K. Gupta & S. Saha Ray, 2014. "Wavelet Methods for Solving Fractional Order Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-11, May.
    2. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.
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