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

10/02/2019

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by   Hidenori Ogata, et al.

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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.