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A tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity

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  • Wang, Yihong
  • Cao, Jianxiong

Abstract

In this paper, we first propose a tailored finite point method (TFPM) for solving time fractional subdiffusion problems with anisotropic and discontinuous diffusivity. This numerical scheme can perfectly capture the rapid transition of the solutions which contain sharp interface layers even with coarse meshes. Second, the accuracy and stability of the proposed scheme are strictly analyzed. Finally, some numerical examples are provided to show the accuracy and reliability of this new scheme.

Suggested Citation

  • Wang, Yihong & Cao, Jianxiong, 2021. "A tailored finite point method for subdiffusion equation with anisotropic and discontinuous diffusivity," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    • Handle: RePEc:eee:apmaco:v:401:y:2021:i:c:s0096300320308602
    DOI: 10.1016/j.amc.2020.125907
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    References listed on IDEAS

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    1. Yang, Tinggan & Wang, Yihong, 2019. "A new tailored finite point method for strongly anisotropic diffusion equation on misaligned grids," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 85-95.
    2. Baseri, A. & Abbasbandy, S. & Babolian, E., 2018. "A collocation method for fractional diffusion equation in a long time with Chebyshev functions," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 55-65.
    3. Luo, Wei-Hua & Huang, Ting-Zhu & Wu, Guo-Cheng & Gu, Xian-Ming, 2016. "Quadratic spline collocation method for the time fractional subdiffusion equation," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 252-265.
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