Fast integration for Cauchy principal value integrals of oscillatory kind

DOI10.1007/s10440-012-9709-zzbMath1259.65053OpenAlexW1996550962MaRDI QIDQ1937988

Ru-yun Chen

Publication date: 1 February 2013

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-012-9709-z

zbMATH Keywords

Cauchy principal valueconvergencenumerical experimentserror boundsnumerical quadratureHermite interpolationoscillatory integrand

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (14)

Numerical evaluation of oscillatory-singular integrals ⋮ Numerical methods for Cauchy principal value integrals of oscillatory Bessel functions ⋮ Fast computation of a class of highly oscillatory integrals ⋮ Asymptotics and numerical approximation of highly oscillatory Hilbert transforms ⋮ On quadrature of highly oscillatory integrals with logarithmic singularities ⋮ Numerical approximations of highly oscillatory Hilbert 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 ⋮ An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application ⋮ Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels ⋮ Approximation of Cauchy-type singular integrals with high frequency Fourier kernel ⋮ Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands ⋮ On fast multipole methods for Fredholm integral equations of the second kind with singular and highly oscillatory kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Note on the homotopy perturbation method for multivariate vector-value oscillatory integrals
• Efficient Filon-type methods for \(\int_a^b f(x)\,e^{i\omega g(x)}\, dx\)
• A parameter method for computing highly oscillatory integrals
• Uniform approximations to Cauchy principal value integrals of oscillatory functions
• Numerical solution of the Hilbert transform for phase calculation from an amplitude spectrum
• On quadrature for Cauchy principal value integrals of oscillatory functions.
• A numerical approach to principal value integrals in despersion relations
• On quadrature methods for highly oscillatory integrals and their implementation
• Quadrature Formulae for Cauchy Principal Value Integrals of Oscillatory Kind
• A Fourier series method for numerical Kramers-Kronig analysis
• Efficient quadrature of highly oscillatory integrals using derivatives

This page was built for publication: Fast integration for Cauchy principal value integrals of oscillatory kind