Some quadrature methods for general and singular integrals in one and two dimensions
thesisposted on 2018-04-06, 08:43 authored by Vincent U. Aihie
In this thesis numerical integration in one and two dimensions is considered. In chapter two transformation methods are considered primarily for singular integrals and methods of computing the transformations themselves are derived. The well-known transformation based on the IMT rule and error function are extended to non-standard functions. The implementation of these rules and their performances are demonstrated. These transformations are then extended to two-dimensions and are used to develop accurate rules for integrating singular integrals. In addition to this, a polynomial transformation with the aim of the reduction in the number of function evaluations is also considered and the resultant product rule is applied to two-dimensional non-singular integrals. Finally, the use of monomials in the construction of integration rules for non-singular two-dimensional integrals is considered and some rules developed. In all these situations the rules developed are tested and compared with existing methods. The results show that the new rules compare favourably with existing ones.
- Mathematical Sciences
Publisher© Vincent U. Aihie
Publisher statementThis 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/
NotesA Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.