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On the computation of highly oscillatory multivariate integrals with stationary points |
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| Authors: | A. Iserles S. P. Nørsett |
| Affiliation: | (1) Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom;(2) Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway |
| 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. In memory of Germund Dahlquist (1925–2005). AMS subject classification (2000) Primary 65D32 |
| Keywords: | numerical quadrature asymptotic methods high oscillation |
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