On the numerical calculation of Hadamard finite-part integrals

Abstract

In this paper we consider a simple method for calculating integrals possessing strong singularities, to be interpreted in the Hadamard finite-part sense. We partition the original interval of integration and then integrate over the subintervals by using suitably modified low-order Gaussian-type quadratures. Convergence is shown under suitable assumptions and numerical evidence supports the theoretical findings.

Keywords

• Numerical integration
• Quadrature formulae
• Hadamard finite pert integrals
• Hypersingular integrals