An extrapolation procedure for the evaluation of singular integrals

DOI10.1080/00207168208803342zbMath0518.65008OpenAlexW2010588606MaRDI QIDQ3667839

A. P. G. Morgan, J. Hyslop, Gwynne Evans

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1080/00207168208803342

zbMATH Keywords

convergenceerror estimationnumerical testsextrapolation procedureepsilon algorithmcontinued fraction transformationPatterson quadraturecritical comparisonsfinite range singular integralspseudo-Gaussian quadrature formulaequadrature series

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Extrapolation to the limit, deferred corrections (65B05) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (4)

Extrapolation methods in numerical integration ⋮ Polynomial transformations for singular integrals ⋮ The asymptotic expansion and extrapolation of trapezoidal rule for integrals with fractional order singularities ⋮ The tanh transformation for singular integrals

Cites Work

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• A method for numerical integration on an automatic computer
• Comparison of some methods for evaluating infinite range oscillatory integrals
• Accelerated convergence of sequences of quadrature approximations
• Cautious romberg extrapolation
• A comment on quadrature in the presence of end point singularities
• A quadrature method for finite intervals
• Extension of numerical quadrature formulae to cater for end point singular behaviours over finite intervals
• Development of non-linear transformations for improving convergence of sequences
• Integration Formulae Based on the Trapezoidal Formula

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