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On the design and implementation of a hybrid numerical method for singularly perturbed two-point boundary value problems
(University of the Western Cape, 2014)
With the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these ...
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 ...
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 ...
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 ...