Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm

DOI10.1016/j.cam.2019.02.012zbMath1415.65059OpenAlexW2921332250MaRDI QIDQ2000630

Takemitsu Hasegawa, Sugiura, Hiroshi

Publication date: 28 June 2019

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.2019.02.012

zbMATH Keywords

error analysisquadrature ruleuniform approximationChebyshev interpolationoscillatory functionprincipal value integral

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (11)

Numerical methods for Cauchy principal value integrals of oscillatory Bessel functions ⋮ Interpolation based formulation of the oscillatory finite Hilbert transforms ⋮ Asymptotics and numerical approximation of highly oscillatory Hilbert transforms ⋮ Numerical approximations of highly oscillatory Hilbert transforms ⋮ Adaptive FCC+ rules for oscillatory integrals ⋮ Approximation of oscillatory Bessel integral transforms ⋮ Efficient computation of oscillatory Bessel transforms with a singularity of Cauchy type ⋮ Efficient computational methods of highly oscillatory Bessel transforms with a singular point of Cauchy type and a nonlinear special oscillator ⋮ Efficient numerical methods for hypersingular finite-part integrals with highly oscillatory integrands ⋮ Numerical steepest descent method for Hankel type of hypersingular oscillatory integrals in electromagnetic scattering problems ⋮ Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands

Uses Software

• mctoolbox
• Clenshaw-Curtis

Cites Work

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