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Iteration methods for Fredholm integral equations of the second kind based on spline quasi-interpolants

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  • Allouch, C.
  • Sablonnière, P.

Abstract

In this paper, we propose an efficient iteration algorithm for Fredholm integral equations of the second kind based on spline quasi-interpolants (abbr. QIs). We show that for every iteration step we obtain superconvergence rates. A superconvergent method called functional approximation method based on QIs is also developed. We illustrate our results by numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:99:y:2014:i:c:p:19-27
    DOI: 10.1016/j.matcom.2013.04.014
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    References listed on IDEAS

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    1. Allouch, C. & Sablonnière, P. & Sbibih, D., 2011. "A modified Kulkarni's method based on a discrete spline quasi-interpolant," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1991-2000.
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    Cited by:

    1. Barrera, D. & El Mokhtari, F. & Ibáñez, M.J. & Sbibih, D., 2020. "A quasi-interpolation product integration based method for solving Love’s integral equation with a very small parameter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 213-223.
    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. Bellour, A. & Sbibih, D. & Zidna, A., 2016. "Two cubic spline methods for solving Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 1-11.

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