Thesis-1998-Chung.pdf (5.18 MB)
Computing oscillatory integrals by complex methods
thesis
posted on 2018-05-31, 14:56 authored by Kwok-Chiu ChungThe 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. ChungPublisher 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
1998Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en