Numerical integration of oscillatory Airy integrals with singularities on an infinite interval

DOI10.1016/j.cam.2017.11.009zbMath1380.65057OpenAlexW2768935978MaRDI QIDQ679595

Hongchao Kang

Publication date: 11 January 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.11.009

zbMATH Keywords

numerical exampleasymptotic expansionsrecurrence relationsinfinite intervalFilon-type methodsFast Fourier transformClenshaw-Curtis-Filon-type methodshighly oscillatory Airy integralsMeijer G-functions

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

Related Items (8)

Numerical evaluation of oscillatory-singular integrals ⋮ Fast non-polynomial interpolation and integration for functions with logarithmic singularities ⋮ An efficient quadrature rule for the oscillatory infinite generalized Bessel transform with a general oscillator and its error analysis ⋮ Numerical evaluation and error analysis of many different oscillatory Bessel transforms via confluent hypergeometric function ⋮ Efficient calculation and asymptotic expansions of many different oscillatory infinite integrals ⋮ Asymptotic analysis and numerical methods for oscillatory infinite generalized Bessel transforms with an irregular oscillator ⋮ Spectral Levin-type methods for calculation of generalized Fourier transforms ⋮ Approximation of highly oscillatory integrals containing special functions

Uses Software

• DLMF
• MeijerG

Cites Work

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