English

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

Numerical Analysis 2019-09-20 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.1909.08872,
  title  = {A numerical method for Hadamard finite-part integrals with an integral power singularity at an endpoint},
  author = {Hidenori Ogata},
  journal= {arXiv preprint arXiv:1909.08872},
  year   = {2019}
}

Comments

10 pages, 2 figures