Automatic generation of quadrature formulae for oscillatory integrals

Open Access
Publisher Website
Google Scholar
Abstract
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.

This publication has 0 references indexed in Scilit: