Numerical method for computing Hadamard finite-part integrals with a non-integral power singularity at an endpoint

In this paper, we propose a numerical method of computing a Hadamard finite-part integral with a non-integral power singularity at an endpoint, that is, a finite part of a divergent integral 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 formula. Theoretical error estimate and some numerical examples show the effectiveness of the proposed method.Comment: 9 pages, 2 figures, 1 tabl

A numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval

In this paper, we propose a numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval, that is, a finite value assigned to a divergent integral with an integral power singularity at the endpoint on a half infinite interval. In the proposed method, we express a desired finite-part integral using a complex integral, and we obtain the integral by evaluating the complex integral by the DE formula. Theoretical error estimate and some numerical examples show the effectiveness of the proposed method.Comment: 10 pages, 3 figure

Numerical method of computing Hadamard finite-part integrals with a non-integral power singularity at the endpoint over a half infinite interval

In this paper, we propose a numerical method of computing an Hadamard finite-part integral, a finite value assigned to a divergent integral, with a non-integral power singularity at the endpoint on a half infinite interval. In the proposed method, we express a desired finite part integral using a complex integral, and we obtain the finite part integral by evaluating the complex integral by the DE formula. Theoretical error estimate and some numerical examples show the exponential convergence of the proposed method.Comment: 11pages, 3 figures. arXiv admin note: text overlap with arXiv:1910.0080

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

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.Comment: 10 pages, 2 figure