A high order, progressive method for the evaluation of irregular oscillatory integrals

A method is presented for the evaluation of rapidly oscillatory integrals. The method is a variation of Levin's method, and involves forming a quadrature rule which is exact for a certain set of functions. It is shown that the choice of exact functions and, more importantly, the integration abscissae are crucial to the convergence and numerical stability of the method. The computation of the integration weights is also discussed. Comparisons are made with alternative methods, in particular with Levin's original implementation. (C) 1997 Elsevier Science B.V.