On the computation of Fourier transforms of singular functions

DOI10.1016/0377-0427(92)90264-XzbMath0762.65099MaRDI QIDQ1195727

Maria Branders, Robert Piessens

Publication date: 18 January 1993

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

zbMATH Keywords

Chebyshev polynomialsnumerical examplesrecurrence relationssingular functionsClenshaw-Curtis quadratureendpoint singularitiesfinite complex Fourier transforms

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (24)

A method for efficient computation of integrals with oscillatory and singular integrand ⋮ Efficient methods for highly oscillatory integrals with weak and Cauchy singularities ⋮ On uniform approximations to hypersingular finite-part integrals ⋮ Asymptotic expansions and fast computation of oscillatory Hilbert transforms ⋮ Efficient integration for a class of highly oscillatory integrals ⋮ An efficient quadrature rule for weakly and strongly singular integrals ⋮ Unnamed Item ⋮ On fast and stable implementation of Clenshaw-Curtis and Fejér-type quadrature rules ⋮ An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application ⋮ On the numerical approximation for Fourier-type highly oscillatory integrals with Gauss-type quadrature rules ⋮ A method for indefinite integration of oscillatory and singular functions ⋮ On the numerical quadrature of weakly singular oscillatory integral and its fast implementation ⋮ On the convergence of the method for indefinite integration of oscillatory and singular functions ⋮ Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels ⋮ Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels ⋮ A Chebyshev collocation method for a class of Fredholm integral equations with highly oscillatory kernels ⋮ Efficient computation of highly oscillatory integrals with weak singularities by Gauss-type method ⋮ Efficient computation of highly oscillatory Fourier-type integrals with monomial phase functions and Jacobi-type singularities ⋮ Spectral Levin-type methods for calculation of generalized Fourier transforms ⋮ Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands ⋮ Computation of integrals with oscillatory singular factors of algebraic and logarithmic type ⋮ Levin methods for highly oscillatory integrals with singularities ⋮ On error bounds of Filon-Clenshaw-Curtis quadrature for highly oscillatory integrals ⋮ On efficient computation of highly oscillatory retarded potential integral equations

Uses Software

• QUADPACK

Cites Work

• Modified Clenshaw-Curtis method for the computation of Bessel function integrals
• Computation of Fourier transform integrals using Chebyshev series expansions
• Construction of a recurrence relation for modified moments
• An extension of Clenshaw-Curtis quadrature
• Numerical solution of integral equations of mathematical physics, using Chebyshev polynomials
• Some remarks on uniform asymptotic expansions for Bessel functions
• The numerical solution of linear recurrence relations
• When Not to Use an Automatic Quadrature Routine
• The evaluation and application of some modified moments
• An extension of Miller's algorithm
• Computational Aspects of Three-Term Recurrence Relations
• On the Construction of Gaussian Quadrature Rules from Modified Moments
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the computation of Fourier transforms of singular functions