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The Computer Journal 1975 18(2):173-176; doi:10.1093/comjnl/18.2.173
© 1975 by British Computer Society
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Automatic generation of quadrature formulae for oscillatory integrals

A. Alaylioglu *, G. A. Evans * and J. Hyslop *

Department of Mathematics, University of Technology, Loughborough, UK

An effective method of generating general quadrature formulae of the Newton-Cotes type is developed and extended to the case of oscillatory integrands where Filon-type formulae are produced. Coefficients of the Newton-Cotes formulae of order n ≤ 10 are reproduced for checking purposes and examples of Filon-type coefficients are quoted. An application of these formulae to the evaluation of an oscillatory integral is presented. A simple method of generating product combinations arising from the Lagrangian interpolation formulae employed is described which forms the basis of the computational method.

Received June 1973.

* Department of Mathematics, University of Technology, Loughborough, Leicestershire LE11 3TU


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