>Magister Scientiae - MSc / In this thesis, we consider some interesting mathematical models arising in
ecology. Our focus is on the exploration of robust numerical solvers which are
applicable to models arising in mathematical ecology. To begin with, we consider
a simple but nonlinear second-order time-dependent partial differential
equation, namely, the Allen-Cahn equation. We discuss the construction of a
class of exponential time differencing methods to solve this particular problem.
This is then followed by a discussion on the extension of this approach
to solve a more difficult fourth-order time-dependent partial differential equation,
namely, Kuramoto-Sivashinsky equation. This equation is nonlinear.
Further applications include the extension of this approach to solve a complex
predator-prey system which is a system of fourth-order time-dependent
non-linear partial differential equations. For each of these differential equation
models, we presented numerical simulation results. / 2025
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uwc/oai:etd.uwc.ac.za:11394/8846 |
| Date | January 2021 |
| Creators | Farah, Gassan Ali Mohamed Osman |
| Contributors | Patidar, Kailash C. |
| Publisher | University of Western Cape |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Rights | University of Western Cape |
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