Numerical evaluation of certain strongly singular integrals

DOI10.1093/imanum/drt017zbMath1292.65025OpenAlexW2116701524MaRDI QIDQ5416819

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Publication date: 15 May 2014

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imanum/drt017

zbMATH Keywords

convergencesingular integralerror estimatesnumerical examplesCauchy principle valueHadamard finite partGaussian quadrature ruleinterpolatory quadrature rulesLagrange-Hermite interpolating polynomial

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Conjugate functions, conjugate series, singular integrals (42A50)

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The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions ⋮ Approximation of Hilbert and Hadamard transforms on \((0,+\infty)\) ⋮ Efficient numerical methods for hypersingular finite-part integrals with highly oscillatory integrands ⋮ Numerical computation of hypersingular integrals on the real semiaxis ⋮ The Cauchy principal value and the Hadamard finite part integral as values of absolutely convergent integrals ⋮ Unified compact numerical quadrature formulas for Hadamard finite parts of singular integrals of periodic functions ⋮ Error bounds for a Gauss-type quadrature rule to evaluate hypersingular integrals

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