New Algorithms to Compute Hypersingular Integrals with Rapidly Oscillating Kernels

The paper is dedicated to the study of two new algorithms for approximating hypersingular integrals with rapidly oscillating kernels. The methods use an interpolatory procedure at zeros of orthogonal polynomials. Estimates of the error are given, as well as of the amplification factors. Some numerical examples show the coherence of the theoretical results with the numerical ones.