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Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions

Author

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  • Zhang, Jiali
  • Fang, Zhi-Wei
  • Sun, Hai-Wei

Abstract

A robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs) is developed, superiorly handling the cases of small or vanishing lower bound of the VO function. The fast finite difference scheme sharp decreases the storage requirement and computational complexity. Significantly, the error estimate for the proposed scheme is studied without any regularity assumptions of the true solution. Numerical experiments are tested to verify the effectiveness of the proposed method.

Suggested Citation

  • Zhang, Jiali & Fang, Zhi-Wei & Sun, Hai-Wei, 2022. "Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003472
    DOI: 10.1016/j.amc.2022.127273
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
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    Cited by:

    1. Tan, Zhijun, 2025. "Second-order non-uniform and fast two-grid finite element methods for non-linear time-fractional mobile/immobile equations with weak regularity," Applied Mathematics and Computation, Elsevier, vol. 486(C).

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