IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v254y2015icp266-276.html
   My bibliography  Save this article

A multigrid preconditioned numerical scheme for a reaction–diffusion system

Author

Listed:
  • Bhowmik, Samir Kumar

Abstract

Reaction diffusion operators have been used to model many engineering and biological systems. In this study we consider a reaction diffusion system modeling various engineering and life science problems. There are many algorithms to approximate such mathematical models. Most of the algorithms are conditionally stable and convergent. For a big time step size a Krylov subspace type solver for such models converges slowly or oscillates because of the presence of the diffusion term. Here we study a multigrid preconditioned generalized minimal residual method (GMRES) for such a model. We start with a five point scheme for the spatial integration and a method of lines for the temporal integration of the system of PDEs. Then we implement a multigrid iterative algorithm for the full discrete model, and show some numerical results to demonstrate the dominance of the solver. We analyze the convergence rate of such a multigrid iterative preconditioning algorithm. Reaction diffusion systems arise in many mathematical models and thus this study has many applicabilities.

Suggested Citation

  • Bhowmik, Samir Kumar, 2015. "A multigrid preconditioned numerical scheme for a reaction–diffusion system," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 266-276.
    • Handle: RePEc:eee:apmaco:v:254:y:2015:i:c:p:266-276
    DOI: 10.1016/j.amc.2014.12.062
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314017160
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.12.062?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.

    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:254:y:2015:i:c:p:266-276. 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.