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Zbl 1030.41016
Cruz-Uribe, D.; Neugebauer, C.J.
Sharp error bounds for the trapezoidal rule and Simpson's rule. (English)
[J] JIPAM, J. Inequal. Pure Appl. Math. 3, No.4, Paper No.49, 22 p., electronic only (2002). ISSN 1443-5756/e

Error bounds for the trapezoidal quadrature rule and Simpson's method are derived under the various (typically weak) smoothness assumptions on the integrand function. Some of the results are closely related to those of {\it P. Köhler} [Math. Res. 86, 141-150 (1995; Zbl 0843.41011), and estimates for linear remainder functionals by the modulus of continuity, in B. Bojanov (ed.), Open problems in approximation theory, SCT Publ.\ Comp., Singapore, 109-124 (1994).
[Kai Diethelm (Braunschweig)]

MSC 2000:: *41A55 Approximate quadratures
26A42 Ordinary integrals of functions of one real variable

Keywords: numerical integration; trapezoidal rule; Simpson's rule

Citations: Zbl 0843.41011

Cited in: Zbl 1213.65048

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