Numerical Integration - A Maple Perspective

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Roumeliotis, John (2003) Numerical Integration - A Maple Perspective. RGMIA research report collection, 6 (3).

Abstract

Peano kernels are most popular for their application in constructing integration rules and (perhaps) more importantly for providing an estimate of the error in the rule. The systematic use of these kernels has produced an abundance of new rules as well as providing many new error bounds for the well known Newton-Cotes quadrature. In this paper we will outline a simple method that uses the computer algebra system Maple that is able to recapture the well known Ostrowksi, trapezoidal and Simpson’s inequalities. Moreover, the technique, which involves manipulation of the Peano kernel, can be adapted to develop new rules, which due to algebraic complexities, have yet to be discovered.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/17848
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords Ostrowksi inequality, trapezoidal inequality, Simpson’s inequalities, Maple, Peano kernels, integration rules
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