On the computation of highly oscillatory multivariate integrals with stationary points
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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 wordsnumerical quadrature asymptotic methods high oscillation
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