Master of Science
Corless, Robert M.
In this thesis, we examine the main types of numerical quadrature methods for a special subclass of one-dimensional highly oscillatory integrals. Along with a presentation of the methods themselves and the error bounds, the thesis contains implementations of the methods in Maple and Python. The implementations take advantage of the symbolic computational abilities of Maple and allow for a larger class of problems to be solved with greater ease to the user. We also present a new variation on Levin integration which uses differentiation matrices in various interpolation bases.
Trivedi, Jeet, "A Survey Of Numerical Quadrature Methods For Highly Oscillatory Integrals" (2019). Electronic Thesis and Dissertation Repository. 6182.