Browsing Philosophiae Doctor  PhD (Mathematics) by Title
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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 reactiondiffusion problems arising in biology
(2013)In this thesis, we solve some timedependent partial differential equations, and systems of such equations, that governs reactiondiffusion 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 ... 
Fischerclifford 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 BlackScholes equations and their robust numerical simulations
(University of Western Cape, 2020)Conventional partial differential equations under the classical BlackScholes approach have been extensively explored over the past few decades in solving option pricing problems. However, the underlying Efficient Market ... 
Fractional blackscholes equations and their robust numerical simulations
(University of the Western Cape, 2020)Conventional partial differential equations under the classical BlackScholes 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 mdimensional 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 ... 
A mathematical model for studying the impact of climate variability on malaria epidemics in South Africa
(University of the Western Cape, 2017)Malaria is most prevalent in tropical climates, where there are sufficient rainfall for mosquitoes to breed and conducive temperatures for both the mosquito and protozoa to live. A slight change in temperature can ... 
Mathematical modeling of TB disease dynamics in a crowded population.
(University of the Western Cape, 2020)Tuberculosis is a bacterial infection which is a major cause of death worldwide. TB is a curable disease, however the bacterium can become resistant to the first line treatment against the disease. This leads to a disease ... 
Mathematical modeling of the transmission dynamics of malaria in South Sudan
(University of the Western Cape, 2019)Malaria is a common infection in tropical areas, transmitted between humans through female anopheles mosquito bites as it seeks blood meal to carry out egg production. The infection forms a direct threat to the lives of ... 
Mathematical models for optimal management of bank capital, reserves and liquidity
(University of the Western Cape, 2019)The aim of this study is to construct and propose continuoustime mathematical models for optimal management of bank capital, reserves and liquidity. This aim emanates from the global financial crisis of 2007 − 2009. In ... 
Measurements of edge uncolourability in cubic graphs
(University of the Western Cape, 2020)The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the ... 
Mesh free methods for differential models in financial mathematics
(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 ... 
Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance
(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 ... 
On the primarity of some block intersection graphs
(University of the Western Cape, 2018)A tactical con guration consists of a nite set V of points, a nite set B of blocks and an incidence relation between them, so that all blocks are incident with the same number k points, and all points are incident with ... 
Optimal asset allocation and capital adequacy management strategies for Basel III compliant banks
(University of the Western Cape, 2015)In this thesis we study a range of related commercial banking problems in discrete and continuous time settings. The ﬁrst problem is about a capital allocation strategy that optimizes the expected future value of a commercial ...