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Numerical studies of reaction-diffusion in physiological processes
Thesis (DSc)--University of Pretoria, 1980.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613475617898496 |
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| access_status_str | Open Access |
| author2 | Snyman, Johannes Arnoldus |
| author_browse | Snyman, Johannes Arnoldus |
| author_facet | Snyman, Johannes Arnoldus |
| collection | Thesis |
| dc_rights_str_mv | © 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. |
| description | Thesis (DSc)--University of Pretoria, 1980. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/85322 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:44.480Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/85322 Numerical studies of reaction-diffusion in physiological processes Snyman, Johannes Arnoldus Meiring, Anna Francina UCTD Numerical studies reaction-diffusion physiological processes Thesis (DSc)--University of Pretoria, 1980. The 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. Mathematics and Applied Mathematics DSc Unrestricted 2022-05-17T11:20:10Z 2022-05-17T11:20:10Z 2021/11/03 1980 Thesis * https://repository.up.ac.za/handle/2263/85322 en © 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. application/pdf University of Pretoria |
| spellingShingle | UCTD Numerical studies reaction-diffusion physiological processes Numerical studies of reaction-diffusion in physiological processes |
| title | Numerical studies of reaction-diffusion in physiological processes |
| title_full | Numerical studies of reaction-diffusion in physiological processes |
| title_fullStr | Numerical studies of reaction-diffusion in physiological processes |
| title_full_unstemmed | Numerical studies of reaction-diffusion in physiological processes |
| title_short | Numerical studies of reaction-diffusion in physiological processes |
| title_sort | numerical studies of reaction diffusion in physiological processes |
| topic | UCTD Numerical studies reaction-diffusion physiological processes |
| url | https://repository.up.ac.za/handle/2263/85322 |