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The Computer Journal 1969 12(2):179-182; doi:10.1093/comjnl/12.2.179
© 1969 by British Computer Society
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The evaluation of definite integrals by interval subdivision

H. O'Hara and F. J. Smith *

Departments of Computer Science and Applied Mathematics, The Queen's University of Belfast, Belfast, UK

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.

Received September 1968.

* Departments of Computer Science and Applied Mathematics, The Queen's University of Belfast, N. Ireland


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