Numerical method for computing Hadamard finite-part integrals with a non-integral power singularity at an endpoint
Numerical Analysis
2019-09-26 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.1909.11398,
title = {Numerical method for computing Hadamard finite-part integrals with a non-integral power singularity at an endpoint},
author = {Hidenori Ogata},
journal= {arXiv preprint arXiv:1909.11398},
year = {2019}
}
Comments
9 pages, 2 figures, 1 table