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Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings
Thesis (DSc (Applied Mathematics))--University of Pretoria, 1981.
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| Format: | Thesis |
| Language: | Afr |
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University of Pretoria
2024
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| _version_ | 1867613481688104960 |
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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 | © 2024 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 (Applied Mathematics))--University of Pretoria, 1981. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/99505 |
| institution | University of Pretoria (South Africa) |
| language | Afr |
| last_indexed | 2026-06-10T12:36:50.456Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| 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:2263/99505 Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings Snyman, Johannes Arnoldus Van Niekerk, Frederik Devillebois Eindige-element ydafhanklike parsiele differensiaalvergelykings UCTD Thesis (DSc (Applied Mathematics))--University of Pretoria, 1981. This thesis is concerned with the numerical solutions of time-dependent differential equations by finite element methods. The solutions are approximated by finite elements which depend on both space and time variables. A new Galerkin method is formulated in which the deviations of the approximate solution in both space and time are simultaneously minimized in some sense. The investigation of the new method is mainly of a numerical and experimental nature. Where the analytical solutions of the problems considered are available, they are compared to the numerical solutions. If such solutions are not available then the numerical results will be compared to the solutions obtained by other known numerical methods. Firstly, a survey of finite element methods which are presently used to solve boundary value problems is presented. The Galerkin method and variations thereof will be emphasized. Next, we consider the application of finite element methods to onedimentional problems by using basis functions which are naturally dependent on time only. A step-by-step method is developed which forms the basis for a step-by-step method for two-dimensional problems. A generalisation of the one-step method leads to a Galerkin method in which the basic functions are dependent on both space and time variables. The method is applied to: (i) The heat equation with Dirichlet boundary conditions (ii) The convection-diffusion equation with periodic, Dirichlet and Neumann boundary conditions. In conclusion we apply this method to~ (i) The wave equation with Dirichlet boundary conditions and various different initial conditions. (ii) The wave equation with coupled boundary conditions. Mathematics and Applied Mathematics DSc (Applied Mathematics) 2024-11-27T09:16:02Z 2024-11-27T09:16:02Z 22/02/02 1981 Thesis http://hdl.handle.net/2263/99505 Afr © 2024 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 | Eindige-element ydafhanklike parsiele differensiaalvergelykings UCTD Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings |
| title | Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings |
| title_full | Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings |
| title_fullStr | Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings |
| title_full_unstemmed | Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings |
| title_short | Eindige-element-metodes vir tydafhanklike parsiele differensiaalvergelykings |
| title_sort | eindige element metodes vir tydafhanklike parsiele differensiaalvergelykings |
| topic | Eindige-element ydafhanklike parsiele differensiaalvergelykings UCTD |
| url | http://hdl.handle.net/2263/99505 |