Algorithms for approximating finite Hilbert transform with end-point singularities and its derivatives

DOI10.1016/j.cam.2011.06.027zbMath1236.65158OpenAlexW2022800596MaRDI QIDQ645708

Takemitsu Hasegawa, Sugiura, Hiroshi

Publication date: 10 November 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2011.06.027

zbMATH Keywords

algorithmnumerical examplesHilbert transformquadrature ruleChebyshev interpolationCauchy principal value integralend-point singularities of Jacobi typeHadamard finite-part integralshyper-singular integrals

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (2)

The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions ⋮ Approximating the finite Hilbert transform via some companions of Ostrowski's inequalities

Uses Software

• Clenshaw-Curtis

Cites Work

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• A method for numerical integration on an automatic computer
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• Generalized Chebyshev Interpolation and Its Application to Automatic Quadrature
• Error Bounds for Gaussian Quadrature of Analytic Functions
• Numerical Solution of Sigular Integral Equations Using Gauss-type Formulae I
• On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives
• An Automatic Quadrature for Cauchy Principal Value Integrals
• Truncation Errors in Two Chebyshev Series Approximations
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Implementing Clenshaw-Curtis quadrature, I methodology and experience

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