Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions. A MATLAB toolbox, IIPBF, for calculating infinite integrals involving a product of two Bessel functions J a (ρx)J b (τx),J a (ρx)Y b (τx) and Y a (ρx)Y b (τx), for non-negative integers a,b, and a well-behaved function f(x), is described. Based on the Lucas algorithm previously developed for J a (ρx)J b (τx) only, IIPBF recasts each product as the sum of two functions whose oscillatory behavior is exploited in the three-step procedure of adaptive integration, summation, and extrapolation. The toolbox uses customised QUADPACK and IMSL functions from a MATLAB conversion of the SLATEC library. In addition, MATLAB’s own quadgk function for adaptive Gauss-Kronrod quadrature results in a significant speed up compared with the original algorithm. Usage of IIPBF is described and eighteen test cases illustrate the robustness of the toolbox; five additional ones are used to compare IIPBF with the BESSELINT code for rational and exponential forms of f(x) with J a (ρx)J b (τx). Reliability for a broad range of values of ρ and τ for the three different product types as well as different orders in one case is demonstrated. An electronic appendix provides a novel derivation of formulae for five cases.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 9 articles , 1 standard article )

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  1. Liu, Heng; Cai, Yingchun; Zhong, Yang; Pan, Baofeng: Thermo-hydro-mechanical response of a multi-layered pavement with imperfect interface based on dual variable and position method (2021)
  2. Mehdizadeh, Delaram; Eskandari-Ghadi, Morteza; Rahimian, Mohammad: A 3D BEM-FEM approach using layered transversely isotropic half-space Green’s functions in the frequency domain for SSI analyses (2021)
  3. Pan, Ernian; Lin, Chih-Ping; Zhou, Jiangcun: Fundamental solution of general time-harmonic loading over a transversely isotropic, elastic and layered half-space: an efficient and accurate approach (2021)
  4. Sugiura, Hiroshi; Hasegawa, Takemitsu: A truncated Clenshaw-Curtis formula approximates integrals over a semi-infinite interval (2021)
  5. Zhang, Zhiqing; Pan, Ernian: Vertical vibration of a rigid circular disc embedded in a transversely isotropic and layered poroelastic half-space (2020)
  6. Zhang, Zhiqing; Pan, Ernian: Time-harmonic response of transversely isotropic and layered poroelastic half-spaces under general buried loads (2020)
  7. Zhang, Zhiqing; Pan, Ernian: Vertical and torsional vibrations of an embedded rigid circular disc in a transversely isotropic multilayered half-space (2019)
  8. Moshtagh, Ehsan; Pan, Ernian; Eskandari-Ghadi, Morteza: Shear excitation of a multilayered magneto-electro-elastic half-space considering a vast frequency content (2018)
  9. Ratnanather, J. Tilak; Kim, Jung H.; Zhang, Sirong; Davis, Anthony M. J.; Lucas, Stephen K.: Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions (2014)