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A Collocation Method for Mixed Volterra–Fredholm Integral Equations of the Hammerstein Type

Author

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  • Sanda Micula

    (Department of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania)

Abstract

This paper presents a collocation method for the approximate solution of two-dimensional mixed Volterra–Fredholm integral equations of the Hammerstein type. For a reformulation of the equation, we consider the domain of integration as a planar triangle and use a special type of linear interpolation on triangles. The resulting quadrature formula has a higher degree of precision than expected, leading to a collocation method that is superconvergent at the collocation nodes. The convergence of the method is established, as well as the rate of convergence. Numerical examples are considered, showing the applicability of the proposed scheme and the agreement with the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3044-:d:895672
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    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. & 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.
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