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Second-Order Finite Difference/Spectral Element Formulation for Solving the Fractional Advection-Diffusion Equation

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Abstract

The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equation. The time variable has been discretized by a second-order finite difference procedure. The stability and the convergence of the semi-discrete formula have been proven. Then, the spatial variable of the main PDEs is approximated by the spectral element method. The convergence order of the fully discrete scheme is studied. The basis functions of the spectral element method are based upon a class of Legendre polynomials. The numerical experiments confirm the theoretical results.

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Acknowledgements

The authors are grateful to the two reviewers for carefully reading this paper and for their comments and suggestions which have highly improved the paper.

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  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran

    Mostafa Abbaszadeh & Hanieh Amjadian

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  1. Mostafa Abbaszadeh
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  2. Hanieh Amjadian
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Correspondence to Mostafa Abbaszadeh.

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Abbaszadeh, M., Amjadian, H. Second-Order Finite Difference/Spectral Element Formulation for Solving the Fractional Advection-Diffusion Equation. Commun. Appl. Math. Comput. 2, 653–669 (2020). https://doi.org/10.1007/s42967-020-00060-y

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  • DOI: https://doi.org/10.1007/s42967-020-00060-y

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