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Moment-free numerical approximation of highly oscillatory integrals with stationary points

Published online by Cambridge University Press:  01 August 2007

SHEEHAN OLVER
SHEEHAN OLVER*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, UK email: s.olver@damtp.cam.ac.uk
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Abstract

This article presents a method for the numerical quadrature of highly oscillatory integrals with stationary points. We begin with the derivation of a new asymptotic expansion, which has the property that the accuracy improves as the frequency of oscillations increases. This asymptotic expansion is closely related to the method of stationary phase, but presented in a way that allows the derivation of an alternate approximation method that has similar asymptotic behaviour, but with significantly greater accuracy. This approximation method does not require moments.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 4 , August 2007 , pp. 435 - 447
Copyright
Copyright © Cambridge University Press 2007

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