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Superconvergent numerical methods based on bivariate spline quasi-interpolant for solving two-dimensional Hammerstein integral equations

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  • Sennour, M.
  • Tahrichi, M.

Abstract

In this paper, we develop and analyze two superconvergent numerical methods, the degenerate kernel and Nyström methods, for solving two-dimensional Hammerstein integral equations of the second kind. By employing quadratic and Schoenberg–Marsden spline quasi-interpolants, the proposed methods achieve convergence orders of up to eight for the iterated solutions. Numerical experiments show excellent agreement with the theoretical predictions, confirming the high accuracy and efficiency of the proposed methods.

Suggested Citation

  • Sennour, M. & Tahrichi, M., 2026. "Superconvergent numerical methods based on bivariate spline quasi-interpolant for solving two-dimensional Hammerstein integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 248(C), pages 846-858.
    • Handle: RePEc:eee:matcom:v:248:y:2026:i:c:p:846-858
    DOI: 10.1016/j.matcom.2026.04.047
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    References listed on IDEAS

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    1. Eberhard Zeidler, 1990. "Nonlinear Functional Analysis and its Applications," Springer Books, Springer, number 978-1-4612-0981-2, January.
    2. 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.
    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, January.
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