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Finite difference method for solving fractional differential equations at irregular meshes

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  • Vargas, Antonio M.

Abstract

This paper presents a novel meshless technique for solving a class of fractional differential equations based on moving least squares and on the existence of a fractional Taylor series for Caputo derivatives. A “Generalized Finite Difference” approach is followed in order to derive a simple discretization of the space fractional derivatives. Consistency, stability and convergence of the method are proved. Several examples illustrating the accuracy of the method are given.

Suggested Citation

  • Vargas, Antonio M., 2022. "Finite difference method for solving fractional differential equations at irregular meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 204-216.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:204-216
    DOI: 10.1016/j.matcom.2021.10.010
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    References listed on IDEAS

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    1. Salehi, Younes & Darvishi, Mohammad T. & Schiesser, William E., 2018. "Numerical solution of space fractional diffusion equation by the method of lines and splines," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 465-480.
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    Cited by:

    1. Heydari, M.H. & Razzaghi, M. & Rouzegar, J., 2022. "Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Li, Jin & Su, Xiaoning & Zhao, Kaiyan, 2023. "Barycentric interpolation collocation algorithm to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 340-367.
    3. Yang, Changqing, 2023. "Improved spectral deferred correction methods for fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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