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Linearized transformed L1 finite element methods for semi-linear time-fractional parabolic problems

Author

Listed:
  • Han, Yuxin
  • Huang, Xin
  • Gu, Wei
  • Zheng, Bolong

Abstract

A linearized Galerkin finite element method is presented for numerically solving the semi-linear time-fractional parabolic problems, whose solutions always display a initial weak singularity. The transformed L1 scheme based on a change of variable is used to approximate Caputo derivatives and the finite element approximations to the spatial variables. By the temporal-spatial error splitting argument, unconditionally optimal error estimates of the proposed schemes are proved. Finally, several numerical experiments are given to demonstrate our theoretical results.

Suggested Citation

  • Han, Yuxin & Huang, Xin & Gu, Wei & Zheng, Bolong, 2023. "Linearized transformed L1 finite element methods for semi-linear time-fractional parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004113
    DOI: 10.1016/j.amc.2023.128242
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    References listed on IDEAS

    as
    1. Alquran, Marwan & Al-Khaled, Kamel & Sardar, Tridip & Chattopadhyay, Joydev, 2015. "Revisited Fisher’s equation in a new outlook: A fractional derivative approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 81-93.
    2. She, Mianfu & Li, Dongfang & Sun, Hai-wei, 2022. "A transformed L1 method for solving the multi-term time-fractional diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 584-606.
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    More about this item

    Keywords

    Nonlinear time fractional parabolic equation; Transformed L1 scheme; Linearized Galerkin finite element method; Unconditional convergence;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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