Sinc Nyström Method for Singularly Perturbed Love’s Integral Equation

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.