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On the Quadrature of Multivariate Highly Oscillatory Integrals Over Non-polytope Domains

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Abstract

In this paper, we present a Levin-type method for approximating multivariate highly oscillatory integrals, subject to a non-resonance condition. Unlike existing methods, we do not require the knowledge of moments, which enables us to derive an approximation when the oscillator is complicated, and when the domain is neither a simplex nor a polytope. The accuracy of this method improves as the frequency of oscillations increases. A special case of this method has the property that the asymptotic order increases with each additional sample point.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Rd, Cambridge, CB3 0WA, UK

    Sheehan Olver

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  1. Sheehan Olver
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Correspondence to Sheehan Olver.

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Olver, S. On the Quadrature of Multivariate Highly Oscillatory Integrals Over Non-polytope Domains. Numer. Math. 103, 643–665 (2006). https://doi.org/10.1007/s00211-006-0009-2

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  • DOI: https://doi.org/10.1007/s00211-006-0009-2

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