The evaluation of definite integrals by interval subdivision
Open Access
- 1 February 1969
- journal article
- Published by Oxford University Press (OUP) in The Computer Journal
- Vol. 12 (2) , 179-182
- https://doi.org/10.1093/comjnl/12.2.179
Abstract
An algorithm is described for the efficient and reliable evaluation of badly behaved definite integrals to a prescribed accuracy by concentrating the abscissas near the regions of greatest irregularity in the integrand. This is achieved by subdividing the interval of integration and by using a combination of the 7-point Clenshaw–Curtis quadrature and the 9-point Romberg quadrature in each subinterval. We argue that our algorithm will nearly minimise the number of function evaluations needed to evaluate a badly behaved integral.Keywords
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