Browsing Philosophiae Doctor - PhD (Mathematics) by Title
Now showing items 1-20 of 39
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Analysis and implementation of robust numerical methods to solve mathematical models of HIV and Malaria co-infection
(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 ... -
Analysis and robust simulation of mathematical models of HIV and Leishmaniasis co-infection
(University of the Western Cape, 2022)The purpose of this thesis is the theoretical and numerical study of epidemiological models of Visceral Leishmaniasis (VL) and human immunode ciency virus (HIV) coinfection. We study these models theoretically and design ... -
Analysis and simulation of some ecological models describing weed-water hyacinth dynamics in Lake Tana, Ethiopia
(University of the Western Cape, 2022)The water hyacinth plant is notorious for being the world’s worst aquatic weed. In Ethiopia, it invades lake Tana which is the largest lake in Ethiopia. This is attracting attention of many researchers including mathematical ... -
Analysis of errors in derivatives of trigonometric functions: a case study in an extended curriculum programme
(University of the Western Cape, 2012)The purpose of this study was to explore errors that are displayed by students when learning derivatives of trigonometric functions in an extended curriculum programme. The first aim was to identify errors that are displayed ... -
An analytical model for assessing the knowledge of statistical procedures amongst postgraduate students in a higher educational environment
(University of the Western Cape, 2019)Over the past decades, the use and application of statistical concepts for university students have been a big challenge learned from their previous courses. Aftermath of democracy, South African higher education focused ... -
Codes from uniform subset graphs and cycle products
(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 from maximal subgroups of alternating groups
(University of the Western Cape, 2018)The main theme of this thesis is the construction of linear codes from adjacency matrices or sub-matrices of adjacency matrices of regular graphs. We first examine the binary codes from the row span of biadjacency ... -
Codes, graphs and designs related to iterated line graphs of complete graphs
(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 ... -
Efficient numerical methods based on integral transforms to solve option pricing problems
(University of the Western Cape, 2012)In this thesis, we design and implement a class of numerical methods (based on integral transforms) to solve PDEs for pricing a variety of financial derivatives. Our approach is based on spectral discretization of the ... -
Efficient numerical methods to solve some reaction-diffusion problems arising in biology
(2013)In this thesis, we solve some time-dependent partial differential equations, and systems of such equations, that governs reaction-diffusion models in biology. we design and implement some novel exponential time differencing ... -
Efficient Variable Mesh Techniques to solve Interior Layer Problems
(University of Western Cape, 2020)Singularly perturbed problems have been studied extensively over the past few years from different perspectives. The recent research has focussed on the problems whose solutions possess interior layers. These interior ... -
Elementary logic as a tool in proving mathematical statements
(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 ... -
Fischer-clifford matrices and character tables of inertia groups of maximal subgroups of finite simple groups of extension type
(University of the Western Cape, 2011)The aim of this dissertation is to calculate character tables of group extensions. There are several well–developed methods for calculating the character tables of group extensions. In this dissertation we study the method ... -
Fractional Black-Scholes equations and their robust numerical simulations
(University of Western Cape, 2020)Conventional partial differential equations under the classical Black-Scholes approach have been extensively explored over the past few decades in solving option pricing problems. However, the underlying Efficient Market ... -
Fractional black-scholes equations and their robust numerical simulations
(University of the Western Cape, 2020)Conventional partial differential equations under the classical Black-Scholes approach have been extensively explored over the past few decades in solving option pricing problems. However, the underlying Efficient Market ... -
Graphs of integral distance and their properties
(University of Western Cape, 2021)Understanding the geometries of points in space has been attractive to mathematicians for ages. As a model, twelve years ago, Kurz and Meyer [32] considered point sets in the m-dimensional a ne space Fmq over a nite ... -
High Accuracy Fitted Operator Methods for Solving Interior Layer Problems
(University of the Western Cape, 2020)Fitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor ... -
Higher order numerical methods for singular perturbation problems
(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 ... -
Interior operators and their applications
(University of the Western Cape, 2019)Categorical closure operators were introduced by Dikranjan and Giuli in [DG87] and then developed by these authors and Tholen in [DGT89]. These operators have played an important role in the development of Categorical ... -
Mathematical epidemiology of malaria disease transmission and its optimal control analyses
(University of the Western Cape, 2010)In this thesis, we present and analyse an SEIR (susceptible-exposed infectious-recovered) model for malaria disease transmission. The model consists treatment and control strategies such as the use of bed nets and spray ...
