Three Point Quadrature Rules

Pietro Cerone () and Sever S. Dragomir ()
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Pietro Cerone: Victoria University, School of Communications and Informatics
Sever S. Dragomir: Victoria University, School of Communications and Informatics

Chapter Chapter 3 in Ostrowski Type Inequalities and Applications in Numerical Integration, 2002, pp 141-250 from Springer

Abstract: Abstract A unified treatment of three point quadrature rules is presented in which the classical rules of mid-point, trapezoidal and Simpson type are recaptured as particular cases. Riemann integrals are approximated for the derivative of the integrand belonging to a variety of norms. The Grüss inequality and a number of variants are also presented which provide a variety of inequalities that are suitatable for numerical implementation. Mappings that are of bounded total variation, Lipschitzian and monotonic are also investigated with relation to Riemann-Stieltjes integrals. Explicit a priori bounds are provided allowing the determination of the partition required to achieve a prescribed error tolerance. It is demonstrated that with the above classes of functions, the average of a mid-point and trapezoidal type rule produces the best bounds.

Keywords: Trapezoidal Rule; Quadrature Rule; Integral Inequality; Point Quadrature; Type Rule (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2519-4_3

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DOI: 10.1007/978-94-017-2519-4_3

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