The superconvergence of the composite midpoint rule for the finite-part integral

DOI10.1016/j.cam.2009.09.030zbMath1204.65163OpenAlexW2076507625MaRDI QIDQ2654203

Zihuan Dai, Xiaoping Zhang, Jiming Wu

Publication date: 15 January 2010

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.2009.09.030

zbMATH Keywords

error estimatesnumerical examplessuperconvergencefinite-part integralfinite-part integral equationcomposite midpoint rule

Mathematics Subject Classification ID

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

Related Items (9)

The adaptive composite trapezoidal rule for Hadamard finite-part integrals on an interval ⋮ Compact numerical quadrature formulas for hypersingular integrals and integral equations ⋮ FINITE PART INTEGRALS ASSOCIATED WITH RIESZ AND HILFER DERIVATIVES ⋮ Numerical solution of a certain hypersingular integral equation of the first kind ⋮ Martensen splines and finite-part integrals ⋮ A fourth order product integration rule by using the generalized Euler-Maclaurin summation formula ⋮ \(L_2\) error estimates of collocation methods for solving certain singular integral equations ⋮ The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals ⋮ Unified compact numerical quadrature formulas for Hadamard finite parts of singular integrals of periodic functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Definitions, properties and applications of finite-part integrals
• On the approximate computation of certain strongly singular integrals
• The numerical evaluation of Hadamard finite-part integrals
• Numerical evaluation of hypersingular integrals
• Sigmoidal transformations and the Euler-Maclaurin expansion for evaluating certain Hadamard finite-part integrals
• Uniform approximations to finite Hilbert transform and its derivative.
• On the computation of the Euler constant \({\gamma}\)
• Superconvergence of the composite Simpson's rule for a certain finite-part integral and its applications
• Analysis of some computational schemes for a hypersingular integral equation on an interval
• Toeplitz-type approximations to the Hadamard integral operator and their applications to electromagnetic cavity problems
• The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval
• Newton-Cotes formulae for the numerical evaluation of certain hypersingular integrals
• Hypersingular integral equations and the theory of wire antennas
• The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals
• Evaluations of certain hypersingular integrals on interval
• Newton-Cotes rules for Hadamard finite-part integrals on an interval
• Interpolatory quadrature rules for Hadamard finite-part integrals and their superconvergence
• On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives
• Evaluations of hypersingular integrals using Gaussian quadrature
• A superconvergence result for the second-order Newton-Cotes formula for certain finite-part integrals
• Two trigonometric quadrature formulae for evaluating hypersingular integrals
• HYPERSINGULAR INTEGRALS: HOW SMOOTH MUST THE DENSITY BE?
• Improvement of the asymptotic behaviour of the Euler–Maclaurin formula for Cauchy principal value and Hadamard finite‐part integrals
• Gauss quadrature rules for finite part integrals

This page was built for publication: The superconvergence of the composite midpoint rule for the finite-part integral