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

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. (c) 2021 Elsevier Ltd. All rights reserved.

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This article presents a numerical method for solving a fractional-order Advection-Dispersion equation (FADE) by utilizing the Caputo operator of fractional differentiation and orthogonal polynomials of the shifted Vieta-Fibonacci polynomials. The main problem is converted into a system of ordinary differential equations, which are then transformed into algebraic equations through spectral collocation technique and non-standard finite difference method. Convergence analysis and error estimate of the suggested method are investigated with numerical applications to demonstrate its applicability and accuracy.