IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v275y2016icp404-410.html
   My bibliography  Save this article

The Pearcey integral in the highly oscillatory region

Author

Listed:
  • López, José L.
  • Pagola, Pedro J.

Abstract

We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. Then we consider here the modified saddle point method introduced in [Lopez, Pérez and Pagola, 2009] [4]. With this method, the analysis is simpler and it is possible to derive a complete asymptotic expansion of P(x, y) for large |y|. The asymptotic analysis requires the study of three different regions for argy separately. In the three regions, the expansion is given in terms of inverse powers of y2/3 and the coefficients are elementary functions of x. The accuracy of the approximation is illustrated with some numerical experiments.

Suggested Citation

  • López, José L. & Pagola, Pedro J., 2016. "The Pearcey integral in the highly oscillatory region," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 404-410.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:404-410
    DOI: 10.1016/j.amc.2015.11.080
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315015829
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.11.080?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.

    Citations

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


    Cited by:

    1. Ferreira, Chelo & López, José L. & Pérez Sinusía, Ester, 2018. "The asymptotic expansion of the swallowtail integral in the highly oscillatory region," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 837-845.

    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:275:y:2016:i:c:p:404-410. 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.