ANZIAM J. 45(E) ppE41--E56, 2004.

A corrected quadrature formula and applications

Nenad Ujevic

A. J. Roberts

(Received 26 March 2003; revised 13 February 2004)

Abstract

A straightforward three-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives.

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Authors

Nenad Ujevic: Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia. mailto:ujevic@mapmf.pmfst.hr
A. J. Roberts: Dept Maths \& Computing, University of Southern Queensland, Toowoomba, Queensland 4352, Australia. mailto:aroberts@usq.edu.au

Published February 17, 2004 ISSN 1446-8735

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Last Modified: Tue Feb 17 9:22:54 2004