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dc.contributor.advisorPatidar, Kailash C.
dc.contributor.authorBashier, Eihab Bashier Mohammed
dc.date.accessioned2014-04-22T10:15:11Z
dc.date.available2014-04-22T10:15:11Z
dc.date.issued2009
dc.identifier.urihttp://hdl.handle.net/11394/3134
dc.descriptionPhilosophiae Doctor - PhDen_US
dc.description.abstractFitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some delay di erential models that arise in biology. Very often such di erential equations are very complex in nature and hence the well-known standard numerical methods seldom produce reliable numerical solutions to these problems. Ine ciencies of these methods are mostly accumulated due to their dependence on crude step sizes and unrealistic stability conditions.This usually happens because standard numerical methods are initially designed to solve a class of general problems without considering the structure of any individual problems. In this thesis, issues like these are resolved for a set of delay di erential equations. Though the developed approaches are very simplistic in nature, they could solve very complex problems as is shown in di erent chapters.The underlying idea behind the construction of most of the numerical methods in this thesis is to incorporate some of the qualitative features of the solution of the problems into the discrete models. Resulting methods are termed as tted numerical methods. These methods have high stability properties, acceptable (better in many cases) orders of convergence, less computational complexities and they provide reliable solutions with less CPU times as compared to most of the other conventional solvers. The results obtained by these methods are comparable to those found in the literature. The other salient feature of the proposed tted methods is that they are unconditionally stable for most of the problems under consideration.We have compared the performances of our tted numerical methods with well-known software packages, for example, the classical fourth-order Runge-Kutta method, standard nite di erence methods, dde23 (a MATLAB routine) and found that our methods perform much better. Finally, wherever appropriate, we have indicated possible extensions of our approaches to cater for other classes of problems. May 2009.en_US
dc.language.isoenen_US
dc.subjectMathematical biologyen_US
dc.subjectDelay di erential equationsen_US
dc.subjectSingular perturbationsen_US
dc.subjectPositivity preserving numerical methodsen_US
dc.subjectBifurcation analysisen_US
dc.subjectFitted operator nite di erence methodsen_US
dc.subjectFitted mesh nite di erence methodsen_US
dc.subjectConvergence analysisen_US
dc.subjectMatrix stability analysisen_US
dc.subjectFourier stability analysisen_US
dc.titleFitted numerical methods for delay differential equations arising in biologyen_US
dc.typeThesisen_US


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