IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v257y2015icp355-364.html
   My bibliography  Save this article

Crank–Nicolson ADI Galerkin finite element method for two-dimensional fractional FitzHugh–Nagumo monodomain model

Author

Listed:
  • Bu, Weiping
  • Tang, Yifa
  • Wu, Yingchuan
  • Yang, Jiye

Abstract

In this paper, a two-dimensional fractional FitzHugh–Nagumo monodomain model (2D-FFHNMM) with zero Dirichlet boundary condition is considered. The model consists of a coupled two-dimensional space fractional nonlinear reaction–diffusion model (2D-SFNRDM) and an ordinary differential equation. The 2D-SFNRDM and ordinary differential equation are decoupled at each time step. A new Crank–Nicolson alternating direction implicit (ADI) Galerkin finite element method for the 2D-SFNRDM is developed. The stability and convergence of the numerical method are discussed. Finally, some numerical examples on 2D-SFNRDM and 2D-FFHNMM are given for verification of our theoretical analysis.

Suggested Citation

  • Bu, Weiping & Tang, Yifa & Wu, Yingchuan & Yang, Jiye, 2015. "Crank–Nicolson ADI Galerkin finite element method for two-dimensional fractional FitzHugh–Nagumo monodomain model," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 355-364.
  • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:355-364
    DOI: 10.1016/j.amc.2014.09.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314012594
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2014.09.034?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhao, Jingjun & Zhang, Yanming & Xu, Yang, 2020. "Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Cheng, Xiujun & Duan, Jinqiao & Li, Dongfang, 2019. "A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 452-464.
    3. Abdelkawy, M.A. & Alyami, S.A., 2021. "Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Hu, Dongdong & Cai, Wenjun & Xu, Zhuangzhi & Bo, Yonghui & Wang, Yushun, 2021. "Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 35-59.

    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:257:y:2015:i:c:p:355-364. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.