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

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

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) + 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.

  • Keywords

Love's integral equation sinc function Nyström method DE-sinc quadrature

  • AMS Subject Headings

45L10 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-48, author = {Fu-Rong Lin, Xin Lu and Xiao-Qing Jin}, 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) + 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.

}, 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 AU - Fu-Rong Lin, Xin Lu & Xiao-Qing Jin JO - East Asian Journal on Applied Mathematics VL - 1 SP - 48 EP - 58 PY - 2018 DA - 2018/02 SN - 3 DO - http://dor.org/10.4208/eajam.291112.220213a UR - https://global-sci.org/intro/article_detail/eajam/10845.html KW - Love's integral equation KW - sinc function KW - Nyström method KW - DE-sinc quadrature AB -

. 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.

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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