A superconvergence result for the second-order Newton–Cotes formula for certain finite-part integrals

In this paper we investigate the superconvergence phenomenon of the second-order quadrature formula of Newton-Cotes type for the computation of finite-part integrals with a second-order singularity on an interval. Superconvergence points are found and a superconvergence estimate is obtained. The validity of the theoretical result is demonstrated by numerical experiments.