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

M. M. Khader and M. Adel
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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

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 09, 1-13

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.

Keywords: The fractional-order Fisher’s equation; the compact finite difference method; Chebyshev-spectral collocation method; convergence and stability analysis (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120501223

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