IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2020i1p65-d470492.html
   My bibliography  Save this article

A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Author

Listed:
  • Benjamin Akers

    (Department of Mathematics and Statistics, Air Force Institute of Technology, Dayton, OH 45433, USA)

  • Tony Liu

    (Department of Mathematics and Statistics, Air Force Institute of Technology, Dayton, OH 45433, USA)

  • Jonah Reeger

    (Independent Researcher, Bellbrook, OH 45305, USA)

Abstract

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R , the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.

Suggested Citation

  • Benjamin Akers & Tony Liu & Jonah Reeger, 2020. "A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation," Mathematics, MDPI, vol. 9(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:65-:d:470492
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/1/65/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/1/65/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kristina O. F. Williams & Benjamin F. Akers, 2023. "Numerical Simulation of the Korteweg–de Vries Equation with Machine Learning," Mathematics, MDPI, vol. 11(13), pages 1-14, June.

    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:9:y:2020:i:1:p:65-:d:470492. 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.