Browsing Faculty of Natural Science by Author "Dept. of Mathematics"
Now showing items 1-20 of 23
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Analysis and implementation of robust numerical methods to solve mathematical models of HIV and Malaria co-infection
Elsheikh, Sara Mohamed Ahmed Suleiman (University of the Western Cape, 2011)There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria ... -
Codes from uniform subset graphs and cycle products
Fish, Washiela (University of the Western Cape, 2007)In this thesis only Binary codes are studied. Firstly, the codes overs the field GF(2) by the adjacency matrix of the complement T(n), ofthe triangular graph, are examined. It is shown that the code obtained is the full ... -
Codes, graphs and designs related to iterated line graphs of complete graphs
Kumwenda, Khumbo (University of the Western Cape, 2011)In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1, 2. In the binary case, results are extended to codes from neighbourhood ... -
Construction and analysis of efficient numerical methods to solve mathematical models of TB and HIV co-infection
Ahmed, Hasim Abdalla Obaid (University of the Western Cape, 2011)The global impact of the converging dual epidemics of tuberculosis (TB) and human immunodeficiency virus (HIV) is one of the major public health challenges of our time, because in many countries, human immunodeficiency ... -
Elementary logic as a tool in proving mathematical statements
May, Bruce Matthew (University of the Western Cape, 2008)The findings of the study indicate that knowledge of logic does help to improve the ability of students to make logical connections (deductions) between and from statements.The results of the study, however, do not indicate ... -
Higher order numerical methods for singular perturbation problems
Munyakazi, Justin Bazimaziki (University of the Western Cape, 2009)In recent years, there has been a great interest towards the higher order numerical methods for singularly perturbed problems. As compared to their lower order counterparts, they provide better accuracy with fewer mesh ... -
Investigating an integrated teaching methodology as a means to prepare students for university studies in mathematics
Ceasar, Reginald Raymon (University of the Western Cape, 2005)A key issue for the success of students entering a first year mathematics course at tertiary level is whether or not they have an integrated understanding and view of the mathematical concepts acquired at school. Various ... -
Mathematical modeling of an epidemic under vaccination in two interacting populations
Ahmed, Ibrahim H.I. (University of the Western Cape, 2011)In this dissertation we present the quantitative response of an epidemic of the so-called SIR-type, in a population consisting of a local component and a migrant component. Each component can be divided into three classes, ... -
A mathematical modeling of optimal vaccination strategies in epidemiology
Nemaranzhe, Lutendo (University of the Western Cape, 2010)We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold ... -
Mesh free methods for differential models in financial mathematics
Sidahmed, Abdelmgid Osman Mohammed (University of the Western Cape, 2011)Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial ... -
A model for managing pension funds with benchmarking in an inflationary market
Nsuami, Mozart (University of the Western Cape, 2011)Aggressive fiscal and monetary policies by governments of countries and central banks in developed markets could somehow push inflation to some very high level in the long run. Due to the decreasing of pension fund benefits ... -
A model of pension portfolios with salary and surplus process
Mtemeri, Nyika (University of the Western Cape, 2010)Essentially this project report is a discussion of mathematical modelling in pension funds, presenting sections from Cairns, A.J.D., Blake, D., Dowd, K., Stochastic lifestyling: Optimal dynamic asset allocation for defined ... -
The non-cancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group
Mkiva, Soga Loyiso Tiyo (University of the Western Cape, 2008)The groups we consider in this study belong to the class X0 of all nitely generated groups with nite commutator subgroups. We shall eventually narrow down to the groups of the form T owZn for some n 2 N and some nite ... -
Numerical methods for the valuation of financial derivatives
Ntwiga, Davis Bundi (University of the Western Cape, 2005)Numerical methods form an important part of the pricing of financial derivatives and especially in cases where there is no closed form analytical formula. We begin our work with an introduction of the mathematical tools ... -
Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance
Khabir, Mohmed Hassan Mohmed (University of the Western Cape, 2011)Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be ... -
Numerical Treatment of Non-Linear singular pertubation problems
Shikongo, Albert (University of the Western Cape, 2007)This thesis deals with the design and implementation of some novel numerical methods for non-linear singular pertubations problems (NSPPs). It provide a survey of asymptotic and numerical methods for some NSPPs in the past ... -
Pairings of Binary reflexive relational structures
Chishwashwa, Nyumbu (University of the Western Cape, 2008)The main purpose of this thesis is to study the interplay between relational structures and topology , and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations ... -
Placing the dead: the spatial distribution and spread of HIV in a major South African city
Rama, Parbavati (University of the Western Cape, 2005)The aim of this study was to establish a new understanding of the epidemiology of HIV/AIDS at the municipal level, but at the same time upholding the anonymity of the HIV infected and AIDS sufferers. Innovative research ... -
Pricing American style employee stock options having GARCH effects
Arotiba, Gbenga Joseph (University of the Western Cape, 2010)We investigate some simulation-based approaches for the valuing of the employee stock options. The mathematical models that deal with valuation of such options include the work of Jennergren and Naeslund [L.P Jennergren ... -
Robust computational methods for two-parameter singular perturbation problems
Elago, David (University of the Western Cape, 2010)This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov ...