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Zeitschrift für Analysis und ihre Anwendungen


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Volume 11, Issue 1, 1992, pp. 135–141
DOI: 10.4171/ZAA/619

Published online: 1992-03-31

An Explicit Representation of the Remainder of some Newton-Cotes Formulas in Terms of Higher Order Differences

Bernhard Büttgenbach[1], Gerald Lüttgens[2] and Rolf Joachim Nessel[3]

(1) RWTH Aachen, Germany
(2) RWTH Aachen, Germany
(3) RWTH Aachen, Germany

Depending upon the exactness of the rule, the remainders of some Newton-Cotes formulas are explicitly represented in terms of higher order differences. Consequently, those error bounds for the associated compound quadrature processes, given via corresponding moduli of continuity, may now beestablished in a completely elementary way, in fact with good constants. As an application of previous quantitative extensions of the uniform boundedness principle it is finally shown that the error estimates considered are always sharp.

Keywords: error representations, midpoint trapezoidal, Simpson, 3/8-, Milne rule, sharpness of error bounds

Büttgenbach Bernhard, Lüttgens Gerald, Nessel Rolf Joachim: An Explicit Representation of the Remainder of some Newton-Cotes Formulas in Terms of Higher Order Differences. Z. Anal. Anwend. 11 (1992), 135-141. doi: 10.4171/ZAA/619