Magister Scientiae - MSc / Many chemical and physical problems are mathematically described by partial
differential equations (PDEs). These PDEs are often highly nonlinear and
therefore have no closed form solutions. Thus, it is necessary to recourse to
numerical approaches to determine suitable approximations to the solution
of such equations. For solutions possessing sharp spatial transitions (such as
boundary or interior layers), standard numerical methods have shown limitations
as they fail to capture large gradients. The method of lines (MOL)
is one of the numerical methods used to solve PDEs. It proceeds by the
discretization of all but one dimension leading to systems of ordinary di erential
equations. In the case of time-dependent PDEs, the MOL consists of
discretizing the spatial derivatives only leaving the time variable continuous.
The process results in a system to which a numerical method for initial value
problems can be applied. In this project we consider various types of singularly
perturbed time-dependent PDEs. For each type, using the MOL, the
spatial dimensions will be discretized in many different ways following fitted
numerical approaches. Each discretisation will be analysed for stability and
convergence. Extensive experiments will be conducted to confirm the analyses.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uwc/oai:etd.uwc.ac.za:11394/5679 |
| Date | January 2017 |
| Creators | Mbroh, Nana Adjoah |
| Contributors | Munyakazi, Justin Bazimaziki |
| Publisher | University of the Western Cape |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Rights | University of the Western Cape |
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