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

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

Published online: 2018-02

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• 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.

45L10, 65R20

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@Article{EAJAM-3-48, author = {}, title = {Sinc Nyström Method for Singularly Perturbed Love’s Integral Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.291112.220213a}, url = {http://global-sci.org/intro/article_detail/eajam/10845.html} }
TY - JOUR T1 - Sinc Nyström Method for Singularly Perturbed Love’s Integral Equation JO - East Asian Journal on Applied Mathematics VL - 1 SP - 48 EP - 58 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.291112.220213a UR - https://global-sci.org/intro/article_detail/eajam/10845.html KW - Love's integral equation, sinc function, Nyström method, DE-sinc quadrature. AB -

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.

Fu-Rong Lin, Xin Lu & Xiao-Qing Jin. (1970). Sinc Nyström Method for Singularly Perturbed Love’s Integral Equation. East Asian Journal on Applied Mathematics. 3 (1). 48-58. doi:10.4208/eajam.291112.220213a
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