GENERAL THREE-POINT QUADRATURE FORMULAS OF EULER TYPE

Publisher： Cambridge University Press

E-ISSN： 1446-8735|52|3|309-317

ISSN： 1446-1811

Source： ANZIAM Journal, Vol.52, Iss.3, 2011-12, pp. : 309-317

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Abstract

General three-point quadrature formulas for the approximate evaluation of an integral of a function f over [0,1], through the values f(x), f(1/2), f(1−x), f′(0) and f′(1), are derived via the extended Euler formula. Such quadratures are sometimes called “corrected” or “quadratures with end corrections” and have a higher accuracy than the adjoint classical formulas, which only include the values f(x), f(1/2) and f(1−x) . The Gauss three-point, corrected Simpson, corrected dual Simpson, corrected Maclaurin and corrected Gauss two-point formulas are recaptured as special cases. Finally, sharp estimates of error are given for this type of quadrature formula.

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