IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v248y2026icp794-823.html

Two novel meshless methods for solving general fourth-order PDEs in irregular domains: Applications to plate bending problems

Author

Listed:
  • Lin, Xubo
  • Reutskiy, Sergiy
  • Lin, Ji
  • Lu, Jun

Abstract

This paper presents two RBF-based meshless techniques for solving the fourth-order elliptic partial differential equations (PDEs) in complex geometries. The first method assumes splitting the given equation into a system of two Poisson ones. The second technique directly solves the given PDE of the fourth order if the splitting method does not work. The unifying idea of the both techniques is that the two problems (1) approximation of BC and (2) satisfaction of the governing PDE inside the solution domain are considered separately. Besides, the both techniques utilize series of the so-called modified RBFs (MRBFs) for approximation of the solution inside the solution domain. The direct approach yields a significantly higher accuracy and can be applied to a wide class of plate bending problems. The efficacy of the proposed methodologies is validated by illustrative test cases with different configuration and boundary conditions.

Suggested Citation

  • Lin, Xubo & Reutskiy, Sergiy & Lin, Ji & Lu, Jun, 2026. "Two novel meshless methods for solving general fourth-order PDEs in irregular domains: Applications to plate bending problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 794-823.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:794-823
    DOI: 10.1016/j.matcom.2026.04.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426001722
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.04.029?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:matcom:v:248:y:2026:i:c:p:794-823. 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.