Volume 3, Issue 1
Sinc Nyström Method for Singularly Perturbed Love’s Integral Equation

Fu-Rong Lin ,  Xin Lu and Xiao-Qing Jin

10.4208/eajam.291112.220213a

East Asian J. Appl. Math., 3 (2013), pp. 48-58.

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  • Abstract

. An efficient numerical method is proposed for the solution of Love’s integral equation f (x) + 1 π Z 1 −1 c (x − y) 2 + c 2 f ( y)d y = 1, x ∈ [−1, 1] where c > 0 is a small parameter, by using a sinc Nyström method based on a double exponential transformation. The method is derived using the property that the solution f (x) of Love’s integral equation satisfies f (x) → 0.5 for x ∈ (−1, 1) when the parameter c → 0. Numerical results show that the proposed method is very efficient. AMS subject classifications: 45L10, 65R20 Key words: Love’s integral equation, sinc function, Nyström method, DE-sinc quadrature.

  • History

Published online: 2018-02

  • AMS Subject Headings

45L10, 65R20

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