Dukuza, Kenneth Njengele2016-11-012016-11-012009http://hdl.handle.net/20.500.11837/700In this dissertation we develop efficient new methods and techniques to numerically evaluate integrals of both oscillatory and non-oscillatory kind. We have done a comprehensive literature review on the existing methods and made some modifications to them so as to cope with difficulties such as oscillations and strong singularities. In the numerical algorithms we have used mainly the MATLAB source code. Our results have been compared with well-known methods by renowned authors in this field.engThesis