Extension of numerical quadrature formulae to cater for end point singular behaviours over finite intervals

DOI10.1080/00207167708803139zbMath0401.65017OpenAlexW1986002117MaRDI QIDQ4185729

C. G. Harris, W. A. B. Evans

Publication date: 1977

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207167708803139

zbMATH Keywords

Gauss-Legendre QuadratureComparison of Quadrature FormulaeIntegrands with End Point SingularitiesLogarithmic End Point SingularitiesLogarithmic Plus Inverse Square Root End Point SingularitiesTables of Weights

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (13)

A unified Riemann-Hilbert approach to the analytical determination of zeros of sectionally analytic functions ⋮ The modulation of short waves riding on solitary waves ⋮ In defense of linear quadrature rules ⋮ A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics ⋮ Generalized quadrature rules of Gaussian type for numerical evaluation of singular integrals ⋮ Quadrature of Integrands with a Logarithmic Singularity ⋮ Polynomial transformations for singular integrals ⋮ Computation of the roots of cauchy type principal value integrals ⋮ An integral equation approach to internal (2-layer) solitary waves ⋮ A comment on quadrature in the presence of end point singularities ⋮ Computable error bounds for variational functionals of solutions of a convolution integral equations of the first kind ⋮ An extrapolation procedure for the evaluation of singular integrals ⋮ The tanh transformation for singular integrals

Cites Work

• A conjecture on the convergence of numerical estimates for multidimensional integrals with singular integrands
• Partition-extrapolation methods for numerical quadratures
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