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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Official URL: http://anziamj.austms.org.au/V45/E051/Nenad.pdf
[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.
|Item Type:||Article (Commonwealth Reporting Category C)|
|Additional Information:||See the publisher website for access to full-text: http://anziamj.austms.org.au/V45/E051/Nenad.pdf|
|Uncontrolled Keywords:||quadrature formula|
|Fields of Research (FOR2008):||01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations|
|Subjects:||230000 Mathematical Sciences > 230100 Mathematics|
|Socio-Economic Objective (SEO2008):||UNSPECIFIED|
|Deposited On:||11 Oct 2007 11:18|
|Last Modified:||08 Jun 2012 13:18|
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