Quadrature formulas for oscillatory integral transforms

DOI10.1007/BF01407868zbMath0477.65090MaRDI QIDQ1161048

Roderick Wong

Publication date: 1982

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132802

zbMATH Keywords

error boundsquadrature formulasasymptotic expansionsasymptotic approximationsBessel transformsoscillatory integral transforms

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (13)

Recent advances in asymptotic analysis ⋮ Numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures ⋮ Gaussian rule for integrals involving Bessel functions ⋮ Asymptotic expansions and fast computation of oscillatory Hilbert transforms ⋮ A remedy for the failure of the numerical steepest descent method on a class of oscillatory integrals ⋮ On the numerical approximation for Fourier-type highly oscillatory integrals with Gauss-type quadrature rules ⋮ Orthogonal polynomials (in Matlab) ⋮ Fast computation of Bessel transform with highly oscillatory integrands ⋮ Efficient computation of highly oscillatory integrals with weak singularities by Gauss-type method ⋮ Efficient method for the computation of oscillatory Bessel transform and Bessel Hilbert transform ⋮ Numerical approximations for highly oscillatory Bessel transforms and applications ⋮ Weakly convergent expansions of a plane wave and their use in Fourier integrals ⋮ Orthogonal polynomials - Constructive theory and applications

Cites Work

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• [https://portal.mardi4nfdi.de/wiki/Publication:3272169 Tables of Abscissas and Weights for Numerical Evaluation of Integrals of the Form � ∞ 0 e -x x n f(x) dx]
• Numerical Methods Based on Whittaker Cardinal, or Sinc Functions
• On Generating Orthogonal Polynomials
• Computation of Integrals With Oscillatory and Singular Integrands
• Error Bounds for Asymptotic Expansions of Hankel Transforms
• The Asymptotic Approximation of Certain Integrals
• Efficient Computation of the Complex Error Function
• Tables of Zeros and Gaussian Weights of Certain Associated Laguerre Polynomials and the Related Generalized Hermite Polynomials
• Evaluation of the exponential integral for large complex arguments

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