New algorithms for approximating oscillatory Bessel integrals with Cauchy-type singularities

In this paper, we present an efficient numerical algorithm for approximating integrals involving highly oscillatory Bessel functions with Cauchy-type singularities. By employing the technique of complex line integration, the highly oscillatory Bessel integrals are transformed into oscillatory integr...

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Bibliographic Details
Published in:Results in applied mathematics Vol. 21; p. 100422
Main Authors: Wu, Qinghua, Sun, Mengjun
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2024
Elsevier
Subjects:
Bessel integral
Cauchy-type singularities
Complex integration method
Gauss–Laguerre
65D30
Bessel integral
Complex integration method
Gauss–Laguerre
Cauchy-type singularities
65D32
ISSN:2590-0374, 2590-0374
Online Access:Get full text
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Summary:In this paper, we present an efficient numerical algorithm for approximating integrals involving highly oscillatory Bessel functions with Cauchy-type singularities. By employing the technique of complex line integration, the highly oscillatory Bessel integrals are transformed into oscillatory integrals with a Fourier kernel. When the integration interval does not contain zeros, we use Cauchy’s theorem to transform the integration path to the complex plane and then use the Gaussian–Laguerre formula to compute the integral. For cases in which the integration interval contains zeros, we decompose the integral into two parts: the ordinary and the singular integral. We give a stable recursive formula based on Chebyshev polynomials and Bessel functions for ordinary integrals. For singular integrals, we utilize the MeijerG function for efficient computation. Numerical examples verify the effectiveness of the new algorithm and the fast convergence.
ISSN:2590-0374
2590-0374
DOI:10.1016/j.rinam.2023.100422