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Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations

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  • Saffarian, Marziyeh
  • Mohebbi, Akbar

Abstract

In this paper, we propose an efficient numerical method for the solution of one and two dimensional Riesz space fractional advection–dispersion equation. To this end, we use the Crank–Nicolson scheme to discretize this equation in temporal direction and prove that the semi-discrete scheme is unconditionally stable. Then, we apply the spectral element method in spatial directions and obtain the fully discrete scheme. We present an error estimate for the fully discrete scheme. The presented numerical results demonstrate the accuracy and efficiency of the proposed method in comparison with other schemes in literature.

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  • Saffarian, Marziyeh & Mohebbi, Akbar, 2022. "Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 348-370.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:348-370
    DOI: 10.1016/j.matcom.2021.10.020
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    References listed on IDEAS

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    1. Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
    2. Zhao, Jingjun & Zhang, Yanming & Xu, Yang, 2020. "Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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    Cited by:

    1. Ricardo Mendonça de Moraes & Luan Carlos de Sena Monteiro Ozelim & André Luís Brasil Cavalcante, 2022. "Generalized Skewed Model for Spatial-Fractional Advective–Dispersive Phenomena," Sustainability, MDPI, vol. 14(7), pages 1-19, March.
    2. Biswas, Chetna & Singh, Anup & Chopra, Manish & Das, Subir, 2023. "Study of fractional-order reaction-advection-diffusion equation using neural network method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 15-27.

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