Numerical method of computing Hadamard finite-part integrals with a non-integral power singularity at the endpoint over a half infinite interval
Numerical Analysis
2019-10-10 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1910.04058,
title = {Numerical method of computing Hadamard finite-part integrals with a non-integral power singularity at the endpoint over a half infinite interval},
author = {Hidenori Ogata},
journal= {arXiv preprint arXiv:1910.04058},
year = {2019}
}
Comments
11pages, 3 figures. arXiv admin note: text overlap with arXiv:1910.00807