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Numerical methods of oscillatory Bessel transforms with algebraic and Cauchy singularities

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  • Jia, Yingying
  • Kang, Hongchao

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.

Suggested Citation

  • Jia, Yingying & Kang, Hongchao, 2025. "Numerical methods of oscillatory Bessel transforms with algebraic and Cauchy singularities," Applied Mathematics and Computation, Elsevier, vol. 505(C).
    • Handle: RePEc:eee:apmaco:v:505:y:2025:i:c:s0096300325002498
    DOI: 10.1016/j.amc.2025.129523
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    References listed on IDEAS

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    1. Xu, Zhenhua & Geng, Hongrui & Fang, Chunhua, 2020. "Asymptotics and numerical approximation of highly oscillatory Hilbert transforms," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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