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

D. Barrera, F. El Mokhtari, M.J. Ibáñez and D. Sbibih

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 172, issue C, 213-223

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.

Keywords: Love’s integral equation; Spline quasi-interpolation; Product integration method (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:172:y:2020:i:c:p:213-223

DOI: 10.1016/j.matcom.2019.12.008

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