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The Computer Journal 1971 14(3):301-306; doi:10.1093/comjnl/14.3.301
© 1971 by British Computer Society
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The evaluation of definite integrals using high-order formulae

J. Oliver *

Computing Centre, University of Essex, Colchester, UK

The use of high-order integration formulae in general-purpose library routines is widely discouraged in the literature. The reasons advanced for the recommended preference for the trapezoidal, mid-point and Simpson's rules are here analysed, and found to be either irrelevant to modern computation, or highly inconclusive. Attainable error bounds are presented which help to make high-order formulae equally attractive in problems for which they were formerly regarded as inefficient.

Received September 1969. Revised July 1970.

* Computing Centre, University of Essex, Colchester, Essex


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