2134/33239
Kwok-Chiu Chung
Kwok-Chiu
Chung
Computing oscillatory integrals by complex methods
Loughborough University
2018
untagged
Mathematical Sciences not elsewhere classified
2018-05-31 14:56:13
Thesis
https://repository.lboro.ac.uk/articles/thesis/Computing_oscillatory_integrals_by_complex_methods/9375650
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.]