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A quasi-interpolation product integration based method for solving Love’s integral equation with a very small parameter

Author

Listed:
  • Barrera, D.
  • El Mokhtari, F.
  • Ibáñez, M.J.
  • Sbibih, D.

Abstract

In this paper, we propose a simple and efficient method for numerically solving the following Love’s integral equation u(x)+∫−11dπd2+(x−t)2u(t)dt=1,x∈[−1,1],where d>0 is a very small parameter. We apply the product integration method based on discrete spline quadratic quasi-interpolation, by considering a new unknown function v(x)=u(x)−12, using the property that the solution u(x) of Love’s integral equation satisfies u(x)→12 for x∈(−1,1), when the parameter d→0+. Numerical results are presented to illustrate the efficiency of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:172:y:2020:i:c:p:213-223
    DOI: 10.1016/j.matcom.2019.12.008
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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.
    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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