IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v208y2023icp301-325.html
   My bibliography  Save this article

New stable, explicit, second order hopscotch methods for diffusion-type problems

Author

Listed:
  • Saleh, Mahmoud
  • Kovács, Endre
  • Nagy, Ádám

Abstract

The aim of this paper is to systematically construct and test novel odd–even hopscotch-type numerical algorithms solving the diffusion or heat equation. Among the studied explicit two-stage methods some of them are unconditionally stable and have second order convergence rate in time step size, which is proved analytically as well. We apply the best methods to the nonlinear Fisher’s equation to demonstrate that they work also for nonlinear equations. Then, in order to examine the competitiveness of the new algorithms, we test them for the heat equation against widely used numerical solvers in cases where the media are strongly inhomogeneous and thus the coefficients strongly depend on space. The results suggest that the new methods are significantly more effective than the widely used explicit or implicit methods, especially for extremely large stiff systems.

Suggested Citation

  • Saleh, Mahmoud & Kovács, Endre & Nagy, Ádám, 2023. "New stable, explicit, second order hopscotch methods for diffusion-type problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 301-325.
  • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:301-325
    DOI: 10.1016/j.matcom.2023.01.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423000435
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2023.01.029?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:matcom:v:208:y:2023:i:c:p:301-325. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.