IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v466y2024ics0096300323006276.html
   My bibliography  Save this article

Improved uniform error estimates for the two-dimensional nonlinear space fractional Dirac equation with small potentials over long-time dynamics

Author

Listed:
  • Zhang, Pingrui
  • Jiang, Xiaoyun
  • Jia, Junqing

Abstract

We develop improved uniform error bounds on a second-order Strang splitting method for the long-time dynamics of the nonlinear space fractional Dirac equation (NSFDE) in two dimension (2D) with small electromagnetic potentials. First, a Strang splitting approach is implemented to discretize NSFDE in time. Afterwards the Fourier pseudospectral method is used to complete the discretization of NSFDE in space. With the aid of a second-order Strang splitting approach employed to the Dirac equation, the major local truncation error of the indicated numerical methods is established. Moreover, for the semi-discrete scheme and full-discretization, we rigorously demonstrate the improved, sharp uniform error estimates are O(ετ2) and O(h1m+h2m+ετ2) in virtue of the regularity compensation oscillation (RCO) technique. In the formulations, τ is the time step, hi(i=1,2) stands for spatial sizes in xi-directions, m is dependent on the regularity of solutions, and ε∈(0,1]. In order to verify our error bounds and to illustrate some fascinating long-time dynamical behaviors of the NSFDE with honeycomb lattice potentials for varied ε, numerical investigations are presented.

Suggested Citation

  • Zhang, Pingrui & Jiang, Xiaoyun & Jia, Junqing, 2024. "Improved uniform error estimates for the two-dimensional nonlinear space fractional Dirac equation with small potentials over long-time dynamics," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006276
    DOI: 10.1016/j.amc.2023.128458
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323006276
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128458?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:466:y:2024:i:c:s0096300323006276. 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.