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An efficient method for evaluating the integral of a class of highly oscillatory functions

✍ Scribed by Paul J. Harris; Ke Chen

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
625 KB
Volume
230
Category
Article
ISSN
0377-0427

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✦ Synopsis

Highly oscillatory integrals require special techniques for their effective evaluation. Various studies have been conducted to find computational methods for evaluating such integrals. In this paper we present an efficient numerical method to evaluate a class of generalised Fourier integrals (on a line or a square) with integrands of the form f (x)e ikg(x) , under the assumption that in the domain of integration, both f and g are sufficiently smooth and that g does not have any stationary/critical points. Numerical analysis and results are given to illustrate the effectiveness of our method for computing generalised Fourier integrals.

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