IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4690-d1282925.html
   My bibliography  Save this article

Improving Numerical Accuracy of the Localized Oscillatory Radial Basis Functions Collocation Method for Solving Elliptic Partial Differential Equations in 2D

Author

Listed:
  • Anup Lamichhane

    (School of Science, Technology, and Mathematics, Ohio Northern University, Ada, OH 45810, USA)

  • Balaram Khatri Ghimire

    (Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 39104, USA)

  • Thir Dangal

    (Department of Mathematics, Augusta University, Augusta, GA 30912, USA)

Abstract

Recently, the localized oscillatory radial basis functions collocation method (L-ORBFs) has been introduced to solve elliptic partial differential equations in 2D with a large number of computational nodes. The research clearly shows that the L-ORBFs is very convenient and useful for solving large-scale problems, but this method is numerically less accurate. In this paper, we propose a numerical scheme to improve the accuracy of the L-ORBFs by adding low-degree polynomials in the localized collocation process. The numerical results validate that the proposed numerical scheme is highly accurate and clearly outperforms the results of the L-ORBFs.

Suggested Citation

  • Anup Lamichhane & Balaram Khatri Ghimire & Thir Dangal, 2023. "Improving Numerical Accuracy of the Localized Oscillatory Radial Basis Functions Collocation Method for Solving Elliptic Partial Differential Equations in 2D," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4690-:d:1282925
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4690/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4690/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:11:y:2023:i:22:p:4690-:d:1282925. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.