IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v511y2026ics009630032500462x.html

Superconvergent methods for solving two-dimensional Hammerstein integral equations

Author

Listed:
  • Sennour, M.
  • Sbibih, D.
  • Tahrichi, M.

Abstract

In this paper, we introduce the superconvergent degenerate kernel method and the superconvergent Nyström method for the numerical solution of two-dimensional Hammerstein integral equations of the second kind. By employing piecewise polynomial interpolation of degree r, we prove that, under symmetry conditions on both the triangulation and the interpolation nodes, convergence orders of 2r+3 and 2r+4 are achieved for the approximate solutions and their iterated versions, respectively. Furthermore, we discuss computational aspects related to the construction of the corresponding nonlinear systems, and we present numerical examples to illustrate the theoretical results obtained.

Suggested Citation

  • Sennour, M. & Sbibih, D. & Tahrichi, M., 2026. "Superconvergent methods for solving two-dimensional Hammerstein integral equations," Applied Mathematics and Computation, Elsevier, vol. 511(C).
    • Handle: RePEc:eee:apmaco:v:511:y:2026:i:c:s009630032500462x
    DOI: 10.1016/j.amc.2025.129737
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032500462X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129737?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Micula, Sanda, 2015. "A spline collocation method for Fredholm–Hammerstein integral equations of the second kind in two variables," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 352-357.
    2. 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).
    3. Ravi P. Agarwal & Donal O’Regan & Patricia J. Y. Wong, 1999. "Positive Solutions of Differential, Difference and Integral Equations," Springer Books, Springer, number 978-94-015-9171-3, October.
    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.
    1. 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.
    2. Sanda Micula, 2022. "A Collocation Method for Mixed Volterra–Fredholm Integral Equations of the Hammerstein Type," Mathematics, MDPI, vol. 10(17), pages 1-13, August.
    3. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:511:y:2026:i:c:s009630032500462x. 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.