A sinc quadrature rule for Hadamard finite-part integrals

DOI10.1007/BF01386410zbMath0677.65016OpenAlexW2071638946MaRDI QIDQ1123532

Bernard Bialecki

Publication date: 1990

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133448

zbMATH Keywords

error estimatesnumerical examplesanalytic functionsCauchy principal value integralsHadamard finite-part integralsGauss quadraturessinc quadrature rule

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Hilbert and Hadamard transforms by generalized Chebyshev expansion, Numerical evaluation of hypersingular integrals, The use of Sinc-collocation method for solving Falkner-Skan boundary-layer equation, The numerical solution of third‐order boundary value problems using Sinc‐collocation method, Sinc-collocation method for solving the Blasius equation, Uniform approximations to finite Hilbert transform and its derivative., A new algorithm for Cauchy principal value and Hadamard finite-part integrals, Some new transformation properties of the Nielsen generalized polylogarithm, Collocation method using sinc and rational Legendre functions for solving Volterra's population model, The Cauchy principal value and the Hadamard finite part integral as values of absolutely convergent integrals, Accuracy optimal methods for evaluating hypersingular integrals, A method for the numerical evaluation of a Hadamard finite part integral, The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals, The Gauss-Laguerre quadrature rule for finite-part integrals

Cites Work

• On the weights of certain quadratures for the numerical evaluation of Cauchy principal value integrals and their derivatives
• The numerical evaluation of Hadamard finite-part integrals
• Approximations via Whittaker's cardinal function
• A modified sinc quadrature rule for functions with poles near the arc of integration
• Gauss Type Quadrature Rules for Cauchy Principal Value Integrals
• A Sinc-Hunter Quadrature Rule for Cauchy Principal Value Integrals
• On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives
• On the Convergence of Product Formulas for the Numerical Evaluation of Derivatives of Cauchy Principal Value Integrals