Abstract
The last few years have witnessed substantive developments in the computation of highly oscillatory integrals in one or more dimensions. The availability of new asymptotic expansions and a Stokes-type theorem allow for a comprehensive analysis of a number of old (although enhanced) and new quadrature techniques: the asymptotic, Filon-type and Levin-type methods. All these methods share the surprising property that their accuracy increases with growing oscillation.
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Iserles, A., Nørsett, S., Olver, S. (2006). Highly Oscillatory Quadrature: The Story so Far. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_6
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DOI: https://doi.org/10.1007/978-3-540-34288-5_6
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