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Numerical and theoretical treatment based on the compact finite difference and spectral collocation algorithms of the space fractional-order Fisher’s equation

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  • M. M. Khader

    (Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt2Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia)

  • M. Adel

    (Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt4Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madina, Saudi Arabia)

Abstract

This paper presents an accurate numerical algorithm to solve the space fractional-order Fisher’s equation where the derivative operator is described in the Caputo derivative sense. In the presented discretization process, first, we use the compact finite difference (CFD) for a semi-discrete occurrence in time derivative and implement the Chebyshev spectral collocation method (CSCM) of the third-kind to discretize the spatial fractional derivative. The presented method converts the problem understudy to be a system of algebraic equations which can be easily solved. To study the convergence and stability analysis, some theorems are given with their proofs. A numerical simulation is outputted to test the accuracy and applicability of our presented algorithm.

Suggested Citation

  • M. M. Khader & M. Adel, 2020. "Numerical and theoretical treatment based on the compact finite difference and spectral collocation algorithms of the space fractional-order Fisher’s equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-13, September.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:09:n:s0129183120501223
    DOI: 10.1142/S0129183120501223
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