IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v404y2021ics0096300321003179.html
   My bibliography  Save this article

Superconvergent methods based on quasi-interpolating operators for fredholm integral equations of the second kind

Author

Listed:
  • Allouch, C.
  • Remogna, S.
  • Sbibih, D.
  • Tahrichi, M.

Abstract

In this paper, we apply spline quasi-interpolating operators on a bounded interval to solve numerically linear Fredholm integral equations of second kind by using superconvergent Nyström and degenerate kernel methods introduced in [4]. We give convergence orders associated with approximate solutions and their iterated versions in terms of spline quasi-interpolating order. Moreover, asymptotic expansions at the node/partition points for second kind Fredholm integral equations with Green’s type kernel are obtained in the Nyström method based on quadratic and cubic quasi-interpolants. Therefore, the Richardson extrapolation technique is used to improve the convergence orders. Finally, numerical examples and comparison with existing methods are given to illustrate the theoretical results and to show that the proposed methods improve the convergence orders.

Suggested Citation

  • Allouch, C. & Remogna, S. & Sbibih, D. & Tahrichi, M., 2021. "Superconvergent methods based on quasi-interpolating operators for fredholm integral equations of the second kind," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321003179
    DOI: 10.1016/j.amc.2021.126227
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321003179
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126227?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.

    References listed on IDEAS

    as
    1. Allouch, C. & Sablonnière, P. & Sbibih, D., 2011. "A modified Kulkarni's method based on a discrete spline quasi-interpolant," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1991-2000.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Aimi, A. & Leoni, M.A. & Remogna, S., 2024. "Numerical solution of nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel by spline quasi-interpolating projectors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 183-194.
    2. Sara Remogna & Driss Sbibih & Mohamed Tahrichi, 2023. "Superconvergent Nyström Method Based on Spline Quasi-Interpolants for Nonlinear Urysohn Integral Equations," Mathematics, MDPI, vol. 11(14), pages 1-10, July.

    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.
    1. Allouch, C. & Boujraf, A. & Tahrichi, M., 2019. "Discrete superconvergent degenerate kernel method for Fredholm integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 24-32.
    2. Aimi, A. & Leoni, M.A. & Remogna, S., 2024. "Numerical solution of nonlinear Fredholm–Hammerstein integral equations with logarithmic kernel by spline quasi-interpolating projectors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 183-194.
    3. Barrera, D. & El Mokhtari, F. & Ibáñez, M.J. & Sbibih, D., 2020. "A quasi-interpolation product integration based method for solving Love’s integral equation with a very small parameter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 213-223.
    4. Allouch, C. & Sablonnière, P., 2014. "Iteration methods for Fredholm integral equations of the second kind based on spline quasi-interpolants," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 19-27.

    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:404:y:2021:i:c:s0096300321003179. 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: 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.