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arXiv · 1909.08872

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

Hidenori Ogata
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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.

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Hidenori Ogata. 2019-09-19. A numerical method for Hadamard finite-part integrals with an integral power singularity at an endpoint. https://arxiv.org/abs/1909.08872

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