Browsing Philosophiae Doctor - PhD (Mathematics) by Author "Patidar, Kailash C."
Now showing items 1-15 of 15
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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 ... -
Analysis and robust simulation of mathematical models of HIV and Leishmaniasis co-infection
Adamu, Elias M. (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
Belay, Yeshambel Azene (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 ... -
Efficient numerical methods based on integral transforms to solve option pricing problems
Ngounda, Edgard (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
Matthew, Owolabi Kolade (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
Mbayi, Charles K. (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 ... -
Fractional black-scholes equations and their robust numerical simulations
Nuugulu, Samuel Megameno (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 ... -
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 ... -
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 ... -
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 ... -
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 singular perturbation approaches based on spline approximation methods for solving problems in computational finance
Kabir, 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 ... -
Reliable numerical simulations of problems for pricing real estate derivatives
Dube, Mbakisi (University of the Western Cape, 2022)The globalisation of nancial systems has presented new challenges to investing in real estate assets. For example, any crisis occurring in one real estate market will have an adverse e ect on other markets regardless ... -
Robust computational methods to simulate slow-fast dynamical systems governed by predator-prey models
Mergia, Woinshet D. (University of the Western Cape, 2019)Numerical approximations of multiscale problems of important applications in ecology are investigated. One of the class of models considered in this work are singularly perturbed (slow-fast) predator-prey systems which ... -
Robust Spectral Methods for Solving Option Pricing Problems
Pindza, Edson (University of the Western Cape, 2012)Robust Spectral Methods for Solving Option Pricing Problems by Edson Pindza PhD thesis, Department of Mathematics and Applied Mathematics, Faculty of Natural Sciences, University of the Western Cape Ever since the ...