BIT Numerical Mathematics

, Volume 46, Issue 3, pp 549–566 | Cite as

On the computation of highly oscillatory multivariate integrals with stationary points

  • A. Iserles
  • S. P. Nørsett


We consider two types of highly oscillatory bivariate integrals with a nondegenerate stationary point. In each case we produce an asymptotic expansion and two kinds of quadrature algorithms: an asymptotic method and a Filon-type method. Our results emphasize the crucial role played by the behaviour at the stationary point and by the geometry of the boundary of the underlying domain.

Key words

numerical quadrature asymptotic methods high oscillation 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUnited Kingdom
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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