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

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

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.

Suggested Citation

  • Sweilam, Nasser Hassan & El-Sayed, Adel Abd Elaziz & Boulaaras, Salah, 2021. "Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000898
    DOI: 10.1016/j.chaos.2021.110736
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    References listed on IDEAS

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    1. Owolabi, Kolade M., 2020. "High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    3. Zhou, Fengying & Xu, Xiaoyong, 2016. "The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 11-29.
    4. M. Massabó & R. Cianci & O. Paladino, 2011. "An Analytical Solution of the Advection Dispersion Equation in a Bounded Domain and Its Application to Laboratory Experiments," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-14, January.
    5. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    6. Agarwal, P. & El-Sayed, A.A., 2018. "Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 40-49.
    7. A. H. Bhrawy, 2013. "A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, November.
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    Cited by:

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    2. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.

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