Highly Oscillatory Quadrature: The Story so Far

A. Iserles (), S.P. Nørsett () and S. Olver ()
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A. Iserles: University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences
S.P. Nørsett: Norwegian University of Science and Technology, Department of Mathematical Sciences
S. Olver: University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 97-118 from Springer

Abstract: 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.

Keywords: Asymptotic Expansion; Simplicial Complex; Asymptotic Method; Quadrature Method; Gaussian Quadrature (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/978-3-540-34288-5_6

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