Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique

Nasser Hassan Sweilam, Adel Abd Elaziz El-Sayed and Salah Boulaaras

Chaos, Solitons & Fractals, 2021, vol. 144, issue C

Abstract: In this article, a numerical method for solving a fractional-order Advection-Dispersion equation (FADE) is proposed. The fractional-order derivative of the main problem is presented using the Caputo operator of fractional differentiation. Orthogonal polynomials of the shifted Vieta-Fibonacci polynomials are used as a basis for the desired approximate solution. The main problem is converted into a system of ordinary differential equations. These ODEs system is transformed into algebraic equations through the spectral collocation technique and the non-standard finite difference method. Also, the convergence analysis and the error estimate of the suggested method are investigated. Some numerical applications are introduced to demonstrate the applicability and accuracy of the implemented technique.

Keywords: Fractional-order advection-dispersion equation; Vieta-Fibonacci polynomials; Caputo fractional derivative; Non-standard finite difference method; Spectral collocation method (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000898

DOI: 10.1016/j.chaos.2021.110736

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