- Abstract:
- We present a method for the efficient approximation of integrals with highly oscillatory vector-valued kernels, such as integrals involving Airy functions or Bessel functions. We construct a vector-valued version of the asymptotic expansion, which allows us to determine the asymptotic order of a Levin-type method. Levin-type methods are constructed using collocation, and choosing a basis based on the asymptotic expansion results in an approximation with significantly higher asymptotic order. © 2007 Springer Science + Business Media B.V.
- Publication status:
- Published
- Publisher copy:
- 10.1007/s10543-007-0137-9
-
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- Journal:
- BIT NUMERICAL MATHEMATICS
- Volume:
- 47
- Issue:
- 3
- Pages:
- 637-655
- Publication date:
- 2007-09-05
- DOI:
- EISSN:
-
1572-9125
- ISSN:
-
0006-3835
- URN:
-
uuid:645674cc-4a53-47e1-b5fb-9a0984c1636d
- Source identifiers:
-
28871
- Local pid:
- pubs:28871
- Language:
- English
- Keywords:
- Copyright date:
- 2007
Journal article
Numerical approximation of vector-valued highly oscillatory integrals
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