A numerical method for Hadamard finite-part integrals with an integral power singularity at an endpoint

Abstract

In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method, we express the desired finite-part integral using a complex loop integral, and obtain the finite-part integral by evaluating the complex integral by the trapezoidal rule. Theoretical error estimate and some numerical examples show the effectiveness of the proposed method.