Year: 2013
East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 1 : pp. 48–58
Abstract
An efficient numerical method is proposed for the solution of Love’s integral equation $$f (x) + \frac{1}{π}\int_{-1}^1 \frac{c}{(x-y)^2+c^2} f (y)dy = 1, x ∈ [−1, 1]$$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.291112.220213a
East Asian Journal on Applied Mathematics, Vol. 3 (2013), Iss. 1 : pp. 48–58
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Love's integral equation sinc function Nyström method DE-sinc quadrature.