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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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    Cited by:

    1. Yasmin, Humaira, 2022. "Effect of vaccination on non-integer dynamics of pneumococcal pneumonia infection," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    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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