Applied Mathematics
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Bivariate pseudospectral collocation algorithms for nonlinear partial differential equations.
(2016)Abstract available in PDF file. -
Relativistic radiating stars with generalised atmospheres.
(2010)In this dissertation we construct radiating models for dense compact stars in relativistic astrophysics. We first utilise the standard Santos (1985) junction condition to model Euclidean stars. By making use of the ... -
A comparison study of Chebyshev spectral collocation based methods for solving nonlinear second order evolution equations.
(2015)In this study Spectral Quasilinearisation Method (SQLM) coupled with finite differ- ence and Bivariate Spectral Quasilinearisation Method (BSQLM) in solving second order nonlinear evolution partial differential equations ... -
Wind-wave interactions, density stratification and double diffusive convection in rotating flows.
(2015)Abstract available in PDF file. -
Mathematical modeling of cancer treatments and the role of the immune system response to tumor invasion.
(2015)Despite the success of traditional cancer treatments, a definite cure to several cancers does not exist. Further, the traditional cancer treatments are highly toxic and have a relatively low efficacy. Current research ... -
Using spectral methods on HIV infection with TAT and SSU72 activation.
(2016)HIV dynamics within the host are complex especially when a reservoir of latently infected CD4+ T cells are present. The failure of the immune system and antiviral therapy to suppress the virus has been suggested to be ... -
Using epidemiological mathematical models to understand the transmission dynamics of bovine tuberculosis in buffalo and cattle populations.
(2015)In South Africa, buffalo are the maintenance hosts of Mycobacterium bovis (M. bovis), a pathogen that causes bovine tuberculosis in wildlife and domesticated animals. To understand the transmission dynamics of M. bovis, ... -
Nonclassical solutions of hyperbolic conservation laws.
This dissertation studies the nonclassical shock waves which appears as limits of certain type diffusive-dispersive regularisation to hyperbolic of conservation laws. Such shocks occur very often when the ux function ... -
Educational managers' understanding and experiences of the implementation of inclusive education : evidence from selected urban primary schools in Zimbabwe.
This study focused on the school heads‟ understanding and experiences of the implementation of Inclusive Education in selected urban primary schools in Zimbabwe. The apparent absence of a tentative policy statement that ... -
New realistic solutions for charged matter with an equation of state.
The purpose of this thesis is to provide new exact solutions to the Einstein-Maxwell system which are physically reasonable. We assume that the spacetime is static and spherically symmetric with a charged anisotropic ... -
On singularly perturbed problems and exchange of stabilities.
(2015)Singular perturbation theory has been used for about a century to describe models displaying different timescales, that arise in applied sciences; particularly, models displaying two timescales, namely slow time and fast ... -
New models for quark stars with charge and anisotropy.
(2014)We find new classes of exact solutions for the Einstein-Maxwell field equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field ... -
On the physical viability of horizon-free collapse.
(2015-09-04)The so-called Cosmic Censorship Conjecture has drawn widespread attention amongst astrophysicists and particle physicists. In particular, the end-state of gravitational collapse of a bounded matter distribution is a ... -
Thermal evolution of radiation spheres undergoing dissipative gravitational collapse.
(2015-09-04)In this study we investigate the physics of a relativistic radiating star undergoing dissipative collapse in the form of a radial heat flux. Our treatment clearly demonstrates how the presence of shear affects the collapse ... -
Models in isotropic coordinates with equation of state.
(2015-09-04)In this thesis we consider spacetimes which are static and spherically symmetric related to the Einstein and Einstein-Maxwell system of equations in isotropic coordinates. We study both neutral and charged matter ... -
Optimisation of the population Monte Carlo algorithm : application to cosmology.
(2015-09-04)In this thesis we study the Population Monte Carlo (PMC) algorithm and utilise simulations to improve the efficiency of the algorithm by optimising the algorithm parameters. We then ap ply these optimisation results to ... -
Southern African Large Telescope observations of Sunyaev-Zel'dovich effect selected clusters from the Atacama Cosmology Telescope.
(2014)We present Southern African Large Telescope (SALT) follow-up observations of seven massive clusters detected by the Atacama Cosmology Telescope (ACT) using the Sunyaev-Zel’dovich effect (SZE). We conducted multi-object ... -
Shear-free models for relativistic fluids with heat flow and pressure isotropy.
(2014)We model the interior dynamics of a relativistic radiating fuid in a nonstatic spher- ically symmetric spacetime. The matter distribution takes the form of an imperfect fuid with a nonvanishing radially directed heat ... -
Generalized travelling wave solutions for a microscopic chemotaxis model.
(2014)In biology cell migration is one of the most critical processes, for it is decisive in the mechanisms leading to the beginning of life. The collective migration of cells via wave motion plays a key role in understanding ... -
Differential equations for relativistic radiating stars.
(2013)We consider radiating spherical stars in general relativity when they are conformally flat, geodesic with shear, and accelerating, expanding and shearing. We study the junction conditions relating the pressure to the ...
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