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Computing oscillatory integrals by complex methods

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posted on 31.05.2018 by Kwok-Chiu Chung
The research is concerned with the proposal and the development of a general method for computing rapidly oscillatory integrals with sine and cosine weight integrands of the form f(x) exp(iωq(x)). In this method the interval (finite or infinite) of integration is transformed to an equivalent contour in the complex plane and consequently the problem of evaluating the original oscillatory integral reduces to the evaluation of one or more contour integrals. Special contours, called the optimal contours, are devised and used so that the resulting real integrals are non-oscillatory and have rapidly decreasing integrands towards one end of the integration range. The resulting real integrals are then easily computed using any general-purpose quadrature rule. [Continues.]

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

© K.C. Chung

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

1998

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.

Language

en

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