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A numerical study by using the Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation

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

Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

E-mail Address: mohamed.khader@fsc.bu.edu.eg

E-mail Address: mohamedmbd@yahoo.com

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and

Khaled M. Saad

Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia

Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen

E-mail Address: khaledma_sd@hotmail.com

Corresponding author.

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https://doi.org/10.1142/S1793524518500997Cited by:34 (Source: Crossref)

Abstract

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.

Keywords:

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