IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v210y2023icp593-614.html
   My bibliography  Save this article

Numerical integration rules with improved accuracy close to discontinuities

Author

Listed:
  • Amat, Sergio
  • Li, Zhilin
  • Ruiz-Álvarez, Juan
  • Solano, Concepción
  • Trillo, Juan C.

Abstract

This work is devoted to the construction and analysis of a new nonlinear technique that allows obtaining accurate numerical integrations of any order using data that contains discontinuities, and when the integrand is only known at grid points. The novelty of the technique consists in the inclusion of correction terms with a closed expression that depend on the size of the jumps of the function and its derivatives at the discontinuities, that are supposed to be known. The addition of these terms allows recovering the accuracy of classical numerical integration formulas close to the discontinuities, as these correction terms account for the error that the classical integration formulas commit up to their accuracy at smooth zones. Thus, the correction terms can be added during the integration or as post-processing, which is useful if the main calculation of the integral has been already done using classical formulas. We include several numerical experiments that confirm the theoretical conclusions reached in this article.

Suggested Citation

  • Amat, Sergio & Li, Zhilin & Ruiz-Álvarez, Juan & Solano, Concepción & Trillo, Juan C., 2023. "Numerical integration rules with improved accuracy close to discontinuities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 593-614.
    • Handle: RePEc:eee:matcom:v:210:y:2023:i:c:p:593-614
    DOI: 10.1016/j.matcom.2023.03.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423001374
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.03.032?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.

    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:210:y:2023:i:c:p:593-614. 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.