Two trigonometric quadrature formulae for evaluating hypersingular integrals

DOI10.1002/nme.582zbMath1020.65014OpenAlexW2002898383MaRDI QIDQ4708443

U. Jin Choi, Phil Su Kim

Publication date: 17 June 2003

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.582

zbMATH Keywords

trigonometric interpolationtrigonometric quadraturehypersingular integralscrack problems

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Brittle fracture (74R10) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Integral equations with kernels of Cauchy type (45E05)

Related Items (23)

Quadrature rules for finite element approximations of 1D nonlocal problems ⋮ 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 ⋮ Extrapolation methods to compute hypersingular integral in boundary element methods ⋮ Nodal-type collocation methods for hypersingular integral equations and nonlocal diffusion problems ⋮ An embedded formula of the Chebyshev collocation method for stiff problems ⋮ Regularization of divergent integrals: a comparison of the classical and generalized-functions approaches ⋮ Asymptotic expansions of the error for hyper-singular integrals with an interval variable ⋮ Asymptotic error expansions for hypersingular integrals ⋮ Numerical solution of a certain hypersingular integral equation of the first kind ⋮ A modified Gauss quadrature formula with special integration points for evaluation of quasi-singular integrals ⋮ The extrapolation methods based on Simpson's rule for computing supersingular integral on interval ⋮ 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 ⋮ The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval ⋮ An error embedded method based on generalized Chebyshev polynomials ⋮ Unnamed Item ⋮ Superconvergence of Hermite rule for hypersingular integrals on interval ⋮ Trapezoidal rule for computing supersingular integral on a circle

Cites Work

• On the numerical solution of the finite-part singular integral equations of the first and second kind used in fracture mechanics
• On the Numerical Evaluation of a Class of Finite-Part Integrals
• Unnamed Item
• Unnamed Item

This page was built for publication: Two trigonometric quadrature formulae for evaluating hypersingular integrals