Robust computational methods for two-parameter singular perturbation problems select="/dri:document/dri:meta/dri:pageMeta/dri:metadata[@element='title']/node()"/>

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Show simple item record Elago, D 2013-04-08T13:17:38Z 2013-04-08T13:17:38Z 2013-04-08
dc.description A thesis submitted in partial fulfilment of the requirements for the degree Magister Scientiae in the Department of Mathematics and Applied mathematics, University of the Western cape. en_US
dc.description.abstract This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.
dc.language.iso en en_US
dc.subject Singular perturbations en_US
dc.subject Two-parameter problems en_US
dc.subject Fitted finite difference methods en_US
dc.subject Richardsons extrapolation en_US
dc.subject Bakhvalov mesh en_US
dc.subject Shishkin mesh en_US
dc.subject Error estimates en_US
dc.subject Cenvection-diffusion problems en_US
dc.subject Two-point boundary value problems en_US
dc.subject Convergence analysis en_US
dc.title Robust computational methods for two-parameter singular perturbation problems en_US
dc.type Thesis en_US

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