New error bounds for modified quadrature formulas for Cauchy principal value integrals

DOI10.1016/S0377-0427(97)00045-9zbMath0880.41024MaRDI QIDQ1372054

Kai Diethelm

Publication date: 12 January 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

error boundCauchy principal value integralsPeano kernelPeano constantmodified quadrature formulas

Mathematics Subject Classification ID

Approximate quadratures (41A55)

Related Items (5)

Numerical solution of certain Cauchy singular integral equations using a collocation scheme ⋮ A method for the practical evaluation of the Hilbert transform on the real line ⋮ An efficient method for approximate solution of a singular integral equation with Cauchy kernel ⋮ Approximating Cauchy-type singular integral by an automatic quadrature scheme ⋮ Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach

Cites Work

• On the convergence of the Gauss quadrature rules for Cauchy principal value integrals
• On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals
• The numerical evaluation of one-dimensional Cauchy principal value integrals
• On the numerical integration of certain singular integrals
• Quadrature formulas for Cauchy principal value integrals
• On the evaluation of one-dimensional Cauchy principal value integrals by rules based on cubic spline interpolation
• Modified compound quadrature rules for strongly singular integrals
• Uniform convergence of optimal order quadrature rules for Cauchy principal value integrals
• Asymptotically sharp error estimates for modified compound quadrature formulae for Cauchy principal value integrals
• Peano kernels and bounds for the error constants of Gaussian and related quadrature rules for Cauchy principal value integrals
• Asymptotic behaviour of fixed-order error constants of modified quadrature formulae for Cauchy principal value integrals
• The numerical evaluation of Cauchy principal values of integrals by Romberg integration
• On the convergence of Hunter's quadrature rule for Cauchy principal value integrals
• Error Estimates for Three Methods of Evaluating Cauchy Principal Value Integrals
• ON THE BEST QUADRATURE FORMULA OF THE FORM $ \sum_{k=1}^np_kf(x_k)$ FOR SOME CLASSES OF DIFFERENTIABLE PERIODIC FUNCTIONS
• Integral representations of remainders
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