Compact numerical quadrature formulas for hypersingular integrals and integral equations

DOI10.1007/s10915-012-9610-yzbMath1264.65033OpenAlexW1995272352MaRDI QIDQ1936320

Avram Sidi

Publication date: 4 February 2013

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-012-9610-y

zbMATH Keywords

numerical examplenumerical quadratureasymptotic expansionsRichardson extrapolationhypersingular integral equationsCauchy principal value integraltrapezoidal rulehypersingular integralsmidpoint ruleEuler-Maclaurin expansionsHadamard finite part integral

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items (16)

Superconvergence of Newton-Cotes rule for computing hypersingular integral on a circle ⋮ The practical Gauss type rules for Hadamard finite-part integrals using Puiseux expansions ⋮ Approximation of Hilbert and Hadamard transforms on \((0,+\infty)\) ⋮ A Unified Trapezoidal Quadrature Method for Singular and Hypersingular Boundary Integral Operators on Curved Surfaces ⋮ Spectrally accurate numerical quadrature formulas for a class of algebraically singular periodic Hadamard finite part integrals by regularization ⋮ A product integration rule for hypersingular integrals on \((0,+\infty)\) ⋮ Analysis of errors in some recent numerical quadrature formulas for periodic singular and hypersingular integrals via regularization ⋮ Richardson extrapolation on some recent numerical quadrature formulas for singular and hypersingular integrals and its study of stability ⋮ Unnamed Item ⋮ Unified compact numerical quadrature formulas for Hadamard finite parts of singular integrals of periodic functions ⋮ Exactness and convergence properties of some recent numerical quadrature formulas for supersingular integrals of periodic functions ⋮ Corrected trapezoidal rules for boundary integral equations in three dimensions ⋮ Approximation of Hypersingular Integral Operators With Cauchy Kernel ⋮ \(\mathrm{PVTSI}^{(m)}\): a novel approach to computation of Hadamard finite parts of nonperiodic singular integrals ⋮ Exponential convergence of some recent numerical quadrature methods for Hadamard finite parts of singular integrals of periodic analytic functions ⋮ Spectrally accurate numerical quadrature formulas for a class of periodic Hadamard finite part integrals by regularization

Cites Work

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• Quadrature methods for periodic singular and weakly singular Fredholm integral equations
• Comparison of some numerical quadrature formulas for weakly singular periodic Fredholm integral equations
• Numerical evaluation of hypersingular integrals
• On the numerical solution of hypersingular and singular integral equations on the circle
• Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective
• Interlacing properties of the zeros of the orthogonal polynomials and approximation of the Hilbert transform
• Some numerical algorithms to evaluate Hadamard finite-part integrals
• Euler-Maclaurin expansions for integrals with arbitrary algebraic-logarithmic endpoint singularities
• Asymptotic error expansions for hypersingular integrals
• On the classical solvability of the mixed problem for a second-order one-dimensional hyperbolic equation
• The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval
• The superconvergence of the composite midpoint rule for the finite-part integral
• Euler–Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities
• An Extension of the Euler-Maclaurin Summation Formula to Functions with a Branch Singularity
• A Further Extension of the Euler-Maclaurin Summation Formula
• Practical Extrapolation Methods

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