The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals

DOI10.1007/s00211-005-0647-9zbMath1092.65023OpenAlexW1985281317MaRDI QIDQ2581001

Jiming Wu, Sun, Weiwei

Publication date: 10 January 2006

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

Full work available at URL: https://doi.org/10.1007/s00211-005-0647-9

zbMATH Keywords

integro-differential equationsnumerical resultsintegral equationssuperconvergencehypersingular integralweakly singular kernelscomposite trapezoidal ruleHadamard finite part integral

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) 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 (22)

The adaptive composite trapezoidal rule for Hadamard finite-part integrals on an interval ⋮ The superconvergence of composite Newton-Cotes rules for Hadamard finite-part integral on a circle ⋮ Superconvergence of the composite Simpson's rule for a certain finite-part integral and its applications ⋮ Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals ⋮ The superconvergence of the composite midpoint rule for the finite-part integral ⋮ 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 ⋮ Numerical solution of a certain hypersingular integral equation of the first kind ⋮ The extrapolation methods based on Simpson's rule for computing supersingular integral on interval ⋮ Preconditioning iterative algorithm for the electromagnetic scattering from a large cavity ⋮ Toeplitz-type approximations to the Hadamard integral operator and their applications to electromagnetic cavity problems ⋮ The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application ⋮ The trapezoidal rule for computing supersingular integral on interval ⋮ \(L_2\) error estimates of collocation methods for solving certain singular integral equations ⋮ The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval ⋮ Numerical solution of electromagnetic scattering from a large partly covered cavity ⋮ The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals ⋮ The Cauchy principal value and the Hadamard finite part integral as values of absolutely convergent integrals ⋮ Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals ⋮ Superconvergence of Hermite rule for hypersingular integrals on interval ⋮ Euler-Maclaurin expansions and approximations of hypersingular integrals ⋮ Trapezoidal rule for computing supersingular integral on a circle

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