A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method

M.M. Khader and K.M. Saad

Chaos, Solitons & Fractals, 2018, vol. 110, issue C, 169-177

Abstract: In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. This equation presents the problem of biological invasion and occurs, e.g., in ecology, physiology, and in general phase transition problems and others. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce the proposed problem to a system of ODEs, which is solved by using finite difference method (FDM). Some theorems about the convergence analysis are stated. A numerical simulation and a comparison with the previous work are presented. We can apply the proposed method to solve other problems in engineering and physics.

Keywords: Fractional Fisher equation; Chebyshev polynomials; FDM; Convergence analysis (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:110:y:2018:i:c:p:169-177

DOI: 10.1016/j.chaos.2018.03.018

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