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- Title
On the numerical quadrature of highly‐oscillating integrals I: Fourier transforms.
- Authors
Iserles, Arieh
- Abstract
Highly‐oscillatory integrals are allegedly difficult to calculate. The main assertion of this paper is that that impression is incorrect. As long as appropriate quadrature methods are used, their accuracy increases when oscillation becomes faster and suitable choice of quadrature points renders this welcome phenomenon more pronounced. We focus our analysis on Filon‐type quadrature and analyse its behaviour in a range of frequency regimes for integrals of the form ∫0h f(x)ei ω x w(x)d x, where h>0 is small and |ω | large.
- Subjects
NUMERICAL analysis; CURVE rectification &; quadrature; INTEGRALS; FOURIER transforms; FOURIER analysis
- Publication
IMA Journal of Numerical Analysis, 2004, Vol 24, Issue 3, p365
- ISSN
0272-4979
- Publication type
Article
- DOI
10.1093/imanum/24.3.365