Modified compound quadrature rules for strongly singular integrals

DOI10.1007/BF02276881zbMath0809.41026WikidataQ59411913 ScholiaQ59411913MaRDI QIDQ1332686

Kai Diethelm

Publication date: 1 September 1994

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

Cauchy principal value integralscompound quadrature rulemodified Simpson rulePeano constants

Mathematics Subject Classification ID

Numerical methods for integral transforms (65R10) Approximate quadratures (41A55)

Related Items

The adaptive composite trapezoidal rule for Hadamard finite-part integrals on an interval, Asymptotically sharp error estimates for modified compound quadrature formulae for Cauchy principal value integrals, New error bounds for modified quadrature formulas for Cauchy principal value integrals, The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions, Error expansion of classical mid-point rectangle rule for computing Cauchy principal value integrals on an interval, The trapezoidal rule for computing Cauchy principal value integral on circle, A definiteness criterion for linear functionals and its application to Cauchy principal value quadrature, Numerical evaluation of certain hypersingular integrals using refinable operators, On computing with the Hilbert spline transform, The Hilbert transform of cubic splines, A sinc quadrature subroutine for Cauchy principal value integrals, Simpson's rule to approximate Hilbert integral and its application, The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals, Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach

Uses Software

• Mathematica

Cites Work

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• The numerical evaluation of one-dimensional Cauchy principal value integrals
• On the numerical integration of certain singular integrals
• Quadrature formulas for Cauchy principal value integrals
• Hilbert and Hadamard transforms by generalized Chebyshev expansion
• Gauss Type Quadrature Rules for Cauchy Principal Value Integrals
• On the Numerical Evaluation of Singular Integrals of Cauchy Type
• On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives
• Piecewise-Polynomial Quadratures for Cauchy Singular Integrals
• Error Estimates for Three Methods of Evaluating Cauchy Principal Value Integrals