A corrected quadrature formula and applications

Ujevic, Nenad and Roberts, A. J. (2004) A corrected quadrature formula and applications. ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 45 (E). E41-E56. ISSN 1446-1811

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Abstract

[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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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: See the publisher website for access to full-text: http://anziamj.austms.org.au/V45/E051/Nenad.pdf
Depositing User: epEditor USQ
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 01:18
Last Modified: 08 Jun 2012 03:18
Uncontrolled Keywords: quadrature formula
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
URI: http://eprints.usq.edu.au/id/eprint/2986

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