TY - JOUR
T1 - Asymptotic expansion and quadrature of composite highly oscillatory integrals
AU - Iserles, Arieh
AU - Levin, David
PY - 2010
Y1 - 2010
N2 - We consider in this paper asymptotic and numerical aspects of highly oscillatory integrals of the form, where ω ≫ 1. Such integrals occur in the simulation of electronic circuits, but they are also of independent mathematical interest. The integral is expanded in asymptotic series in inverse powers of ω. This expansion clarifies the behaviour for large ω and also provides a powerful means to design effective computational algorithms. In particular, we introduce and analyse Filon-type methods for this integral.
AB - We consider in this paper asymptotic and numerical aspects of highly oscillatory integrals of the form, where ω ≫ 1. Such integrals occur in the simulation of electronic circuits, but they are also of independent mathematical interest. The integral is expanded in asymptotic series in inverse powers of ω. This expansion clarifies the behaviour for large ω and also provides a powerful means to design effective computational algorithms. In particular, we introduce and analyse Filon-type methods for this integral.
UR - http://www.scopus.com/inward/record.url?scp=78649376978&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-2010-02386-5
DO - 10.1090/S0025-5718-2010-02386-5
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AN - SCOPUS:78649376978
SN - 0025-5718
VL - 80
SP - 279
EP - 296
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 273
ER -