Numerical studies of reaction-diffusion in physiological processes

dc.contributor.advisorSnyman, Johannes Arnoldus
dc.contributor.postgraduateMeiring, Anna Francina
dc.date.accessioned2022-05-17T11:20:10Z
dc.date.available2022-05-17T11:20:10Z
dc.date.created2021/11/03
dc.date.issued1980
dc.descriptionThesis (DSc)--University of Pretoria, 1980.
dc.description.abstractThe aim of this study is to conduct a numerical investigation into mathematical models representing two physiological processes, both being examples of reaction-diffusion processes. The first of these processes comes from the field of population genetics when two types of individuals are allowed to mate at random. The governing equation of the relevant model is Fisher's equation [1] The second process comes from the field of neurobiology and concerns the conduction of an impulse in the nervous system, the principal model being the Hodgkin-Huxley system of differential equations [45] with simplifications due to FitzHugh [28] and Nagumo, Arimoto and Yoshizawa [64]. Chapter 1 is an introductory chapter, introducing the reader to reactiondiffusion equations, mathematical modelling in general and giving an exposition as to the purpose of the present study. In Chapter 2 the relevant two physiological processes are discussed and a description is given of the construction of the mathematical models which represent these processes respectively. Assumptions are motivated and refinements to the original models are discussed. In Chapter 3 a general system of reaction-diffusion equations is given, of which the governing equations of the various models are particular examples. A literature survey is then presented which covers both the pure analytical results and numerical results available on the various models.
dc.description.availabilityUnrestricted
dc.description.degreeDSc
dc.description.departmentMathematics and Applied Mathematics
dc.identifier.citation*
dc.identifier.urihttps://repository.up.ac.za/handle/2263/85322
dc.language.isoen
dc.publisherUniversity of Pretoria
dc.rights© 2020 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.
dc.subjectUCTD
dc.subjectNumerical studies
dc.subjectreaction-diffusion
dc.subjectphysiological processes
dc.titleNumerical studies of reaction-diffusion in physiological processes
dc.typeThesis

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