Numerical methods of oscillatory Bessel transforms with algebraic and Cauchy singularities

Yingying Jia and Hongchao Kang

Applied Mathematics and Computation, 2025, vol. 505, issue C

Abstract: This article proposes and analyzes fast and precise numerical methods for calculating the Bessel integral, which exhibits rapid oscillations and includes algebraic and Cauchy singularities. When a>0, we utilize the numerical steepest descent method with the Gauss-Laguerre quadrature formula to solve it. If a=0, we partition the integral into two parts, solving each part using the modified Filon-type method and the numerical steepest descent method, respectively. Moreover, the strict error analysis with respect to the frequency parameter ω is provided via a plenty of theoretical analysis. Finally, the efficiency and precision of these proposed methods are validated by numerical examples.

Keywords: Algebraic and Cauchy singularities; Bessel function; Numerical steepest descent method; Modified Filon-type method; Error analysis (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:505:y:2025:i:c:s0096300325002498

DOI: 10.1016/j.amc.2025.129523

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