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Numerical approximation of vector-valued highly oscillatory integrals

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

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Publisher copy:
10.1007/s10543-007-0137-9

Authors


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

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