IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v248y2026icp686-712.html

Highly accurate multi-Galerkin method for systems of nonlinear Volterra integral equations based on Kumar–Sloan approach

Author

Listed:
  • Malav, Krishna Murari
  • Kant, Kapil
  • Chakraborty, Samiran
  • Dhar, Joydip

Abstract

In this article, we apply the multi-Galerkin method based on the Kumar–Sloan approach to solve the system of Volterra–Hammerstein integral equations with smooth and weakly singular kernels using piecewise polynomial basis functions. First, we develop the mathematical formulation of the multi-Galerkin method using piecewise polynomial approximation subspace to solve such systems. Then we derive error estimates and establish improved convergence rates. To do this, we construct the uniform mesh for smooth kernels and the graded mesh for weakly singular kernels on [0,1]. Moreover, we show that the Kumar–Sloan-based multi-Galerkin method obtains superconvergence results without using its iterated method. Hence, it is noticed that the multi-Galerkin method demonstrates improved performance over the Galerkin method, while maintaining the same system size for both methods. Finally, numerical results are provided to validate the theoretical findings and confirm the expected convergence rate.

Suggested Citation

  • Malav, Krishna Murari & Kant, Kapil & Chakraborty, Samiran & Dhar, Joydip, 2026. "Highly accurate multi-Galerkin method for systems of nonlinear Volterra integral equations based on Kumar–Sloan approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 686-712.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:686-712
    DOI: 10.1016/j.matcom.2026.05.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426001989
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.05.001?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:686-712. 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.