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High-Order Numerical Method for Solving a Space Distributed-Order Time-Fractional Diffusion Equation

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Abstract

This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the piecewise-quadratic polynomials, we construct the nodal basis functions, and then discretize the multi-term fractional equation by the finite volume method. For the time-fractional derivative, the finite difference method is used. Finally, the iterative scheme is proved to be unconditionally stable and convergent with the accuracy O(σ2 + τ2−β + h3), where τ and h are the time step size and the space step size, respectively. A numerical example is presented to verify the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, China

    Jing Li  (李景), Yingying Yang  (杨莹莹) & Yingjun Jiang  (姜英军)

  2. School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, 4001, Australia

    Libo Feng  (封利波)

  3. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Boling Guo  (郭柏灵)

Authors
  1. Jing Li  (李景)
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  2. Yingying Yang  (杨莹莹)
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  3. Yingjun Jiang  (姜英军)
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  4. Libo Feng  (封利波)
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  5. Boling Guo  (郭柏灵)
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Corresponding author

Correspondence to Jing Li  (李景).

Additional information

The first author is supported by the Natural and Science Foundation Council of China (11771059), Hunan Provincial Natural Science Foundation of China (2018JJ3519) and Scientific Research Project of Hunan Provincial office of Education (20A022).

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Li, J., Yang, Y., Jiang, Y. et al. High-Order Numerical Method for Solving a Space Distributed-Order Time-Fractional Diffusion Equation. Acta Math Sci 41, 801–826 (2021). https://doi.org/10.1007/s10473-021-0311-1

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  • DOI: https://doi.org/10.1007/s10473-021-0311-1

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