IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v248y2026icp727-745.html

Approximate solutions of nonlinear functional Volterra integral equations using ramp basis functions

Author

Listed:
  • Qarehbolagh, Peyman Abolghasemi
  • Bazm, Sohrab

Abstract

A collocation method based on ramp basis functions is proposed for the numerical solution of nonlinear functional Volterra integral equations of Urysohn type. Exploiting the local support of the ramp functions, the resulting collocation system has a lower-triangular structure, which allows the approximate solution to be computed sequentially and avoids the solution of large nonlinear algebraic systems. A convergence analysis is presented, and error estimates are derived under mild regularity assumptions using a nonlinear Gronwall inequality, which guarantee first-order convergence of the method.

Suggested Citation

  • Qarehbolagh, Peyman Abolghasemi & Bazm, Sohrab, 2026. "Approximate solutions of nonlinear functional Volterra integral equations using ramp basis functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 727-745.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:727-745
    DOI: 10.1016/j.matcom.2026.05.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426001990
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.05.002?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.

    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:matcom:v:248:y:2026:i:c:p:727-745. 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.