Construction and analysis of exponential time differencing methods for the robust simulation of ecological models

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dc.contributor.advisorPatidar, Kailash C.
dc.contributor.authorFarah, Gassan Ali Mohamed Osman
dc.date.accessioned2022-03-09T07:11:32Z
dc.date.accessioned2024-10-30T10:24:02Z
dc.date.available2024-10-30T10:24:02Z
dc.date.issued2021
dc.description>Magister Scientiae - MScen_US
dc.description.abstractIn 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.en_US
dc.description.embargo2025
dc.identifier.urihttps://hdl.handle.net/10566/16709
dc.language.isoenen_US
dc.publisherUniversity of Western Capeen_US
dc.rights.holderUniversity of Western Capeen_US
dc.subjectMathematical ecologyen_US
dc.subjectNumerical resultsen_US
dc.subjectNonlinearen_US
dc.subjectAdaptive numerical methodsen_US
dc.subjectMathematical modellingen_US
dc.titleConstruction and analysis of exponential time differencing methods for the robust simulation of ecological modelsen_US

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