East Asian J. Appl. Math., 3 (2013), pp. 48-58.
Published online: 2018-02
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.291112.220213a}, url = {http://global-sci.org/intro/article_detail/eajam/10845.html} }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.