Rees, Tom van (2024) Finding Global Point Symmetries of Partial Differential Equations. Master's Thesis / Essay, Physics.
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Abstract
Lie point symmetries are local symmetries of differential equations that map the set of solutions to itself. The underlying theory, which only allows to find continuous symmetries of infinitesimal transformations, is explained and applied to differential equations like the logistic equation, heat equation and filtration equation. The results are analyzed to check if these Lie point symmetries remain symmetries for non-infinitesimal transformations and possibly form a global symmetry group. It is found that the heat equation contains a local symmetry, which limits the domain of the transformations, restricting the group from being globally defined. However, the symmetry group can be made global when restricting the solution space of the heat equation. Furthermore, an optimization algorithm is constructed and compared against an analytical method to find discrete point symmetries, and is tested on the spherical Burger’s equation, heat equation and the Laplace equation. Using analytical and computational methods, multiple real discrete point transformations were found for the heat equation, with the symmetry group having 4 connected components.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Boer, D. and Aalbers, J. |
| Degree programme: | Physics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 23 Jul 2024 10:17 |
| Last Modified: | 23 Jul 2024 10:17 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33577 |
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