IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i12p2685-d1170263.html
   My bibliography  Save this article

Second-Order Robust Numerical Method for a Partially Singularly Perturbed Time-Dependent Reaction–Diffusion System

Author

Listed:
  • Manikandan Mariappan

    (Department of Mathematics, School of Engineering, Presidency University, Bengaluru 560064, Karnataka, India
    These authors contributed equally to this work.)

  • Chandru Muthusamy

    (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Higinio Ramos

    (Department of Applied Mathematics, Scientific Computing Group, University of Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
    Escuela Politécnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain)

Abstract

This article aims at the development and analysis of a numerical scheme for solving a singularly perturbed parabolic system of n reaction–diffusion equations where m of the equations (with m < n ) contain a perturbation parameter while the rest do not contain it. The scheme is based on a uniform mesh in the temporal variable and a piecewise uniform Shishkin mesh in the spatial variable, together with classical finite difference approximations. Some analytical properties and error analyses are derived. Furthermore, a bound of the error is provided. Under certain assumptions, it is proved that the proposed scheme has almost second-order convergence in the space direction and almost first-order convergence in the time variable. Errors do not increase when the perturbation parameter ε → 0 , proving the uniform convergence. Some numerical experiments are presented, which support the theoretical results.

Suggested Citation

  • Manikandan Mariappan & Chandru Muthusamy & Higinio Ramos, 2023. "Second-Order Robust Numerical Method for a Partially Singularly Perturbed Time-Dependent Reaction–Diffusion System," Mathematics, MDPI, vol. 11(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2685-:d:1170263
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/12/2685/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/12/2685/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:11:y:2023:i:12:p:2685-:d:1170263. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.