Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Spectral difference methods for solving equations of the KdV hierarchy
Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Stellenbosch : Stellenbosch University
2009
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867614102802661376 |
|---|---|
| access_status_str | Open Access |
| author | Pindza, Edson |
| author2 | Maritz, M. F. |
| author_browse | Maritz, M. F. Pindza, Edson |
| author_facet | Maritz, M. F. Pindza, Edson |
| author_sort | Pindza, Edson |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2168 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:46:42.610Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2009 |
| publishDateRange | 2009 |
| publishDateSort | 2009 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2168 Spectral difference methods for solving equations of the KdV hierarchy Pindza, Edson Maritz, M. F. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. Spectral differentiation Dissertations -- Applied mathematics Theses -- Applied mathematics Korteweg-de Vries equation Differential equations, Partial Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008. The Korteweg-de Vries (KdV) hierarchy is an important class of nonlinear evolution equa- tions with various applications in the physical sciences and in engineering. In this thesis analytical solution methods were used to ¯nd exact solutions of the third and ¯fth order KdV equations, and numerical methods were used to compute numerical solutions of these equations. Analytical methods used include the Fan sub-equation method for constructing exact trav- eling wave solutions, and the simpli¯ed Hirota method for constructing exact N-soliton solutions. Some well known cases were considered. The Fourier spectral method and the ¯nite di®erence method with Runge-Kutta time dis- cretisation were employed to solve the third and the ¯fth order KdV equations with periodic boundary conditions. The one soliton and the two soliton solutions were used as initial conditions. The numerical solutions are obtained and compared with the exact solutions. The propagation of a single soliton as well as the interaction of double soliton solutions is modeled well by both numerical methods, although the Fourier spectral method performs better. The stability, consistency and convergence of these numerical methods were investigated. Error propagation is studied. The theoretically predicted quadratic convergence of the ¯nite di®erence method as well as the exponential convergence of the Fourier spectral method is con¯rmed in numerical experiments. 2009-03-04T11:51:01Z 2010-06-01T08:42:01Z 2009-03-04T11:51:01Z 2010-06-01T08:42:01Z 2008-03 Thesis http://hdl.handle.net/10019.1/2168 en Stellenbosch University application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Spectral differentiation Dissertations -- Applied mathematics Theses -- Applied mathematics Korteweg-de Vries equation Differential equations, Partial Pindza, Edson Spectral difference methods for solving equations of the KdV hierarchy |
| title | Spectral difference methods for solving equations of the KdV hierarchy |
| title_full | Spectral difference methods for solving equations of the KdV hierarchy |
| title_fullStr | Spectral difference methods for solving equations of the KdV hierarchy |
| title_full_unstemmed | Spectral difference methods for solving equations of the KdV hierarchy |
| title_short | Spectral difference methods for solving equations of the KdV hierarchy |
| title_sort | spectral difference methods for solving equations of the kdv hierarchy |
| topic | Spectral differentiation Dissertations -- Applied mathematics Theses -- Applied mathematics Korteweg-de Vries equation Differential equations, Partial |
| url | http://hdl.handle.net/10019.1/2168 |
| work_keys_str_mv | AT pindzaedson spectraldifferencemethodsforsolvingequationsofthekdvhierarchy |