IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0327515.html
   My bibliography  Save this article

Besse relaxation difference scheme for a nonlinear integro-differential equation

Author

Listed:
  • Xinya Peng
  • Leiwei Li
  • Jia Zhang

Abstract

In this paper, Besse relaxation difference and compact difference scheme for a nonlinear integro-differential equation, which is crucial in modeling complex systems with memory and nonlocal effects, are proposed. A Besse relaxation difference scheme is developed by combining Besse relaxation time discretization with second-order spatial discretization, in which the Besse relaxation technique enhanced the accuracy and stability of dealing with nonlinear terms. To further improve spatial accuracy, a fourth-order compact finite difference approximation is used to construct the Besse relaxation compact difference scheme. To verify the effectiveness of the proposed Besse relaxation difference schemes, we have established the unconditional stability and optimal convergence of both methods in the discrete L2 norms. Numerical experiments demonstrate that these relaxation schemes attain the predicted convergence rates and high accuracy for smooth solutions, singular solutions, as well as featuring unbounded derivatives solutions.

Suggested Citation

  • Xinya Peng & Leiwei Li & Jia Zhang, 2025. "Besse relaxation difference scheme for a nonlinear integro-differential equation," PLOS ONE, Public Library of Science, vol. 20(8), pages 1-23, August.
    • Handle: RePEc:plo:pone00:0327515
    DOI: 10.1371/journal.pone.0327515
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0327515
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0327515&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0327515?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
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0327515. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.