The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval
From MaRDI portal
Publication:2480888
DOI10.1007/s00211-007-0125-7zbMath1147.65026OpenAlexW2036535859MaRDI QIDQ2480888
Publication date: 3 April 2008
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-007-0125-7
Related Items (39)
The adaptive composite trapezoidal rule for Hadamard finite-part integrals on an interval ⋮ 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 ⋮ Numerical evaluation of highly oscillatory Bessel transforms ⋮ 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 ⋮ Error expansion of classical mid-point rectangle rule for computing Cauchy principal value integrals on an interval ⋮ The trapezoidal rule for computing Cauchy principal value integral on circle ⋮ Error expansion of trapezoidal rule for certain two-dimensional Cauchy principal value integrals ⋮ Nodal-type collocation methods for hypersingular integral equations and nonlocal diffusion problems ⋮ Compact numerical quadrature formulas for hypersingular integrals and integral equations ⋮ On uniform approximations to hypersingular finite-part integrals ⋮ Asymptotic expansions of the error for hyper-singular integrals with an interval variable ⋮ Asymptotic expansion and quadrature rule for a class of singular-oscillatory-Bessel-type transforms ⋮ Numerical solution of a certain hypersingular integral equation of the first kind ⋮ On the evaluation of Bessel transformations with the oscillators via asymptotic series of Whittaker functions ⋮ Martensen splines and finite-part integrals ⋮ The extrapolation methods based on Simpson's rule for computing supersingular integral on interval ⋮ Numerical steepest descent method for Hankel type of hypersingular oscillatory integrals in electromagnetic scattering problems ⋮ Evaluation of Green's boundary formula and its first- and second-order derivatives in Legendre series ⋮ The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application ⋮ On evaluation of Bessel transforms with oscillatory and algebraic singular integrands ⋮ \(L_2\) error estimates of collocation methods for solving certain singular integral equations ⋮ Simpson's rule to approximate Hilbert integral and its application ⋮ Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels ⋮ Error expansion of piecewise constant interpolation rule for certain two-dimensional Cauchy principal value integrals ⋮ The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals ⋮ A numerical study on the stability of a class of Helmholtz problems ⋮ Extended error expansion of classical midpoint rectangle rule for Cauchy principal value integrals on an interval ⋮ Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels ⋮ Unified compact numerical quadrature formulas for Hadamard finite parts of singular integrals of periodic functions ⋮ Numerical approximations for highly oscillatory Bessel transforms and applications ⋮ Nodal-Type Newton-Cotes Rules for Fractional Hypersingular Integrals ⋮ Numerical evaluation and analysis of highly oscillatory singular Bessel transforms with a particular oscillator ⋮ Superconvergence of Hermite rule for hypersingular integrals on interval ⋮ Error bounds for a Gauss-type quadrature rule to evaluate hypersingular integrals ⋮ Euler-Maclaurin expansions and approximations of hypersingular integrals
Cites Work
- 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.
- An additive Schwarz preconditioner for \(p\)-version boundary element approximation of the hypersingular operator in three dimensions
- Newton-Cotes formulae for the numerical evaluation of certain hypersingular integrals
- The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals
- Evaluations of certain hypersingular integrals on interval
- On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives
- Evaluations of hypersingular integrals using Gaussian quadrature
- Spectral Analysis of Hermite Cubic Spline Collocation Systems
- A superconvergence result for the second-order Newton-Cotes formula for certain finite-part integrals
- Two trigonometric quadrature formulae for evaluating hypersingular integrals
- Collocation Methods for Volterra Integral and Related Functional Differential Equations
- Improvement of the asymptotic behaviour of the Euler–Maclaurin formula for Cauchy principal value and Hadamard finite‐part integrals
- Orthogonal spline collocation methods for the stream function‐vorticity formulation of the Navier–Stokes equations
- A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
- Gauss quadrature rules for finite part integrals
This page was built for publication: The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval
