IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v271y2015icp567-580.html
   My bibliography  Save this article

Stability and convergence of radial basis function finite difference method for the numerical solution of the reaction–diffusion equations

Author

Listed:
  • Golbabai, Ahmad
  • Nikpour, Ahmad

Abstract

Stability, convergence and application of radial basis function finite difference (RBF-FD) scheme is studied for solving the reaction–diffusion equations (RDEs). We show that the explicit RBF-FD method is stable, and stability condition depends on the shape parameter of related radial basis function.The generalized multiquadric (GMQ) is applied as radial basis function and weight coefficients are explicitly presented for equispaced node distribution. Also, two methods are presented to compute the optimal shape parameter. The combination of these methods with the GMQ-FD method will produce two efficient algorithms for numerical solution of RDEs: the variable GMQ-FD (VGMQ-FD) and the constant GMQ-FD (CGMQ-FD). We test the scheme on traveling wave and compare its accuracy with the conventional finite difference method (FDM).

Suggested Citation

  • Golbabai, Ahmad & Nikpour, Ahmad, 2015. "Stability and convergence of radial basis function finite difference method for the numerical solution of the reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 567-580.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:567-580
    DOI: 10.1016/j.amc.2015.09.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315012709
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.09.034?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. Asif, Muhammad & Ali Khan, Zar & Haider, Nadeem & Al-Mdallal, Qasem, 2020. "Numerical simulation for solution of SEIR models by meshless and finite difference methods," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Stolbunov, Valentin & Nair, Prasanth B., 2018. "Sparse radial basis function approximation with spatially variable shape parameters," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 170-184.
    3. Li, Yang & Liu, Dejun & Yin, Zhexu & Chen, Yun & Meng, Jin, 2023. "Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    4. Li, Shuling & Li, Xiaolin, 2016. "Radial basis functions and level set method for image segmentation using partial differential equation," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 29-40.

    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:271:y:2015:i:c:p:567-580. 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.