IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p1930-d438871.html
   My bibliography  Save this article

Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

Author

Listed:
  • Zhen Yang

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China)

  • Junjie Ma

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China)

Abstract

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

Suggested Citation

  • Zhen Yang & Junjie Ma, 2020. "Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1930-:d:438871
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/1930/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/1930/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ma, Junjie & Liu, Huilan, 2020. "A sparse fractional Jacobi–Galerkin–Levin quadrature rule for highly oscillatory integrals," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:8:y:2020:i:11:p:1930-:d:438871. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.