IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v320y2018icp27-44.html
   My bibliography  Save this article

Spline reproducing kernels on R and error bounds for piecewise smooth LBV problems

Author

Listed:
  • Andrzejczak, Grzegorz

Abstract

Reproducing kernel method for approximating solutions of linear boundary value problems is valid in Hilbert spaces composed of continuous functions, but its convergence is not satisfactory without additional smoothness assumptions. We prove 2nd order uniform convergence for regular problems with coefficient piecewise of Sobolev class H2. If the coefficients are globally of class H2, more refined phantom boundary NSC-RKHS method is derived, and the order of convergence rises to 3 or 4, according to whether the problem is piecewise of class H3 or H4. The algorithms can be successfully applied to various non-local linear boundary conditions, e.g. of simple integral form.

Suggested Citation

  • Andrzejczak, Grzegorz, 2018. "Spline reproducing kernels on R and error bounds for piecewise smooth LBV problems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 27-44.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:27-44
    DOI: 10.1016/j.amc.2017.09.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317306422
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.09.021?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. Geng, F.Z. & Wu, X.Y., 2021. "Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral," Applied Mathematics and Computation, Elsevier, vol. 397(C).

    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:320:y:2018:i:c:p:27-44. 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.