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

Harris, Paul J. and Chen, Ke (2009) An efficient method for evaluating the integral of a class of highly oscillatory functions Journal of Computational and Applied Mathematics, 230 (2). pp. 433-442. ISSN 0377-0427

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Abstract

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/eikg.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.

Item Type: Journal article
Uncontrolled Keywords: Numerical integration; Oscillatory integrands; High frequency
Subjects: G000 Computing and Mathematical Sciences > G100 Mathematics
DOI (a stable link to the resource): 10.1016/j.cam.2008.12.026
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Computational Mathematics
Depositing User: Paul Harris
Date Deposited: 21 Aug 2009
Last Modified: 21 May 2014 11:01
URI: http://eprints.brighton.ac.uk/id/eprint/5555

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