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On the computation of highly oscillatory multivariate integrals with stationary points

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom

    A. Iserles

  2. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    S. P. Nørsett

Authors
  1. A. Iserles
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  2. S. P. Nørsett
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Corresponding author

Correspondence to S. P. Nørsett.

Additional information

In memory of Germund Dahlquist (1925–2005).

AMS subject classification (2000)

Primary 65D32

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Iserles, A., Nørsett, S. On the computation of highly oscillatory multivariate integrals with stationary points . Bit Numer Math 46, 549–566 (2006). https://doi.org/10.1007/s10543-006-0071-2

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  • DOI: https://doi.org/10.1007/s10543-006-0071-2

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