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

Paul Harris, Ke Chen

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)433-442
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume230
Issue number2
DOIs
Publication statusPublished - Feb 2009

Keywords

  • Numerical integration
  • Oscillatory integrands
  • High frequency

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