Highly oscillatory quadrature: The story so far

Conference item

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. These developments are described in a unified fashion, taking the multivariate integral f(Omega) f (chi)e(iwg(chi))dV as our point of departure.

Authors: Iserles, A; Norsett, S; Olver, S

• Publication status: Published
• Journal: Numerical Mathematics and Advanced Applications
• Pages: 97-118
• Publication date: 2006-01-01
• Event title: 6th European Conference on Numberical Mathematics and Advanced Applications (ENUMATH2005)
• DOI: 10.1007/978-3-540-34288-5_6
• ISBN: 3540342877
• Keywords: DIFFERENTIAL-EQUATIONS; INTEGRALS