Theses And Dissertations

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A Comparative Study of one-step Methods for Numerical Solution of Initial- Value Problems in Ordinary Differential Equations
(University of Fort Hare, 2000-02) Kama, Phumezile
The ultimate aim of the field of Numerical Analysis is to provide a reliable and convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in proper form. It is a common norm that analytic solutions, when available may be very precise in themselves but may be, of course, of unacceptable form because of the fact that they are not amenable to direct interpretation in numerical terms. In which case numerical analyst may attempt to devise a method of effecting that interpretation in a satisfactory way, or he may prefer to base his analysis instead upon the original formulation.
Numerical quadrature of oscillatory and non-oscillatory integrals
(University of Fort Hare, 2009) Dukuza, Kenneth Njengele
In 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.