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Seminar

Numerical approximation of multivariate highly oscillatory integrals

Olver, S (Cambridge)
Wednesday 28 March 2007, 14:30-15:00

Seminar Room 1, Newton Institute

Abstract

The aim of this talk is to describe several methods for numerically approximating the integral of a multivariate highly oscillatory function. We begin with a review of the asymptotic and Filon-type methods developed by Iserles and Nørsett. Using a method developed by Levin as a point of departure we will construct a new method that uses the same information as a Filon-type method, and obtains the same asymptotic order, while not requiring moments. This allows us to integrate over nonsimplicial domains, and with complicated oscillators. We also present a method for approximating oscillatory integrals with stationary points.

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