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Diethdm, K. (1995) Asymptotically Sharp Error Bounds for a Quadrature Rule for Cauchy Principal Value Integrals Based on Piecewise Linear Interpolation, Approx. Theory of Probability and Its Applications, 11, 78-89.

has been cited by the following article:

• TITLE: The Rectangle Rule for Computing Cauchy Principal Value Integral on Circle

  AUTHORS: Jin Li, Benxue Gong, Wei Liu

  KEYWORDS: Cauchy Principal Value Integral, Extrapolation Method, Composite Rectangle Rule, Superconvergence, Error Expansion

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.6 No.2, June 13, 2016

  ABSTRACT: The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.