IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v458y2023ics0096300323004113.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323004113
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128242?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Feng, Libo & Liu, Fawang & Anh, Vo V., 2023. "Galerkin finite element method for a two-dimensional tempered time–space fractional diffusion equation with application to a Bloch–Torrey equation retaining Larmor precession," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 517-537.
    3. Zhou, Yongtao & Li, Mingzhu, 2024. "Error estimate of a transformed L1 scheme for a multi-term time-fractional diffusion equation by using discrete comparison principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 395-404.
    4. Boya Zhou & Xiujun Cheng, 2023. "A Second-Order Time Discretization for Second Kind Volterra Integral Equations with Non-Smooth Solutions," Mathematics, MDPI, vol. 11(12), pages 1-10, June.
    5. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    6. Li, Yuyu & Wang, Tongke & Gao, Guang-hua, 2023. "The asymptotic solutions of two-term linear fractional differential equations via Laplace transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 394-412.
    7. Hu, Zesen & Li, Xiaolin, 2024. "Analysis of a fast element-free Galerkin method for the multi-term time-fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 677-692.
    8. Tan, Zhijun & Zeng, Yunhua, 2024. "Temporal second-order fully discrete two-grid methods for nonlinear time-fractional variable coefficient diffusion-wave equations," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    9. Muhammed I. Syam, 2017. "A Numerical Solution of Fractional Lienard’s Equation by Using the Residual Power Series Method," Mathematics, MDPI, vol. 6(1), pages 1-9, December.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323004113. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.