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 - <p>An efficient numerical method is proposed for the solution of Love’s integral
equation $$f (x) + \frac{1}{π}\int_{-1}^1 \frac{c}{(x-y)^2+c^2}&nbsp;f (y)dy = 1, x ∈ [−1, 1]$$ where $c&gt;0$ 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.&nbsp;</p>