Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels

The Clenshaw-Curtis-type quadrature rule is proposed for the numerical evaluation of the hypersingular integrals with highly oscillatory kernels and weak singularities at the end points (sic)(-1)(1 )(x+1)(alpha)(1-x)(beta)g(x)/(x-s)(m)e(ikx )dx, s is an element of (-1,1) for any smooth functions g(x). Based on the fast Hermite interpolation, this paper provides a stable recurrence relation for these modified moments. Convergence rates with respect to the frequency k and the number of interpolation points N are considered. These theoretical results and high accuracy of the presented algorithm are illustrated by some numerical examples. (C) 2018 Elsevier Inc. All rights reserved.