科研之友
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摘要
We consider in this paper asymptotic and numerical aspects of highly oscillatory integrals of the form integral(b)(a) f(x)g(sin[w theta(x)])dx, where omega >> 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 omega. This expansion clarifies the behaviour for large omega and also provides a powerful means to design effective computational algorithms. In particular, we introduce and analyse Filon-type methods for this integral.
- 出版日期2011-1
