The Cubic Spline Rule for the Hadamard Finite-Part Integral on an Interval

Abstract

We propose a cubic spline rule for the calculation of the Hadamard finite-part integral on an interval. The error estimate is presented in theory, and the superconvergence result of the cubic spline rule for Hadamard finite-part integral is derived. When the singular point coincides with a prior known point, the convergence rate is one order higher than what is globally possible. Numerical experiments are given to demonstrate the efficiency of the theoretical analysis.