A practical algorithm for computing Cauchy principal value integrals of oscillatory functions

DOI10.1016/j.amc.2011.10.064zbMath1246.65257OpenAlexW2025640897MaRDI QIDQ426517

Paweł Keller

Publication date: 11 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.10.064

zbMATH Keywords

algorithmChebyshev polynomialserror analysisquadrature formulauniform approximationCauchy principal value integralsoscillatory integralautomatic integrationClenshaw-Curtis nodesindefinite Cauchy principal value integral

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (20)

Numerical evaluation of oscillatory-singular integrals ⋮ 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 ⋮ On quadrature of highly oscillatory integrals with logarithmic singularities ⋮ Computing Cauchy principal value integrals using a standard adaptive quadrature ⋮ Non-Classical Quadrature Schemes for the Approximation of Cauchy Type Oscillatory and Singular Integrals in Complex Plane ⋮ On uniform approximations to hypersingular finite-part integrals ⋮ 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 ⋮ An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application ⋮ Efficient evaluation of oscillatory Bessel Hilbert transforms ⋮ Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm ⋮ Change of variable formulas for regularizing slowly decaying and oscillatory Cauchy and Hilbert transforms ⋮ On the approximate evaluation of oscillatory-singular integrals ⋮ Extended error expansion of classical midpoint rectangle rule for Cauchy principal value integrals on an interval ⋮ Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels ⋮ Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands ⋮ On the application of GMRES to oscillatory singular integral equations

Uses Software

• Mulprec

Cites Work

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• An Algorithm Based on the FFT for a Generalized Chebyshev Interpolation
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• An Automatic Quadrature for Cauchy Principal Value Integrals
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Implementing Clenshaw-Curtis quadrature, I methodology and experience

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