A numerical study by using the Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation-Reference-Cited by-同舟云学术

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

Published:2018-11 Issue:08 Volume:11 Page:1850099
ISSN:1793-5245
Container-title:International Journal of Biomathematics
language:en
Short-container-title:Int. J. Biomath.

Author:

Khader Mohamed M.¹²,Saad Khaled M.³⁴

Affiliation:

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

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

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793524518500997

Reference31 articles.

1. Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties

2. Explicit solutions of Fisher's equation for a special wave speed

3. Numerical Study of Fisher’s Equation by Finite Difference Schemes

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