Many partial differential equations (PDEs) admit conserved quantities like mass or energy. Those quantities are often essential to establish well-posed results. When approximating a PDE by a finite-difference scheme, it is natural to ask whether related discretized quantities remain conserved under the scheme. Such conservation may establish the stability of the numerical scheme. We present an algorithm for checking the preservation of a polynomial quantity under a polynomial finite-difference scheme. In our algorithm, schemes can be explicit or implicit, have higher-order time and space derivatives, and an arbitrary number of variables. Additionally, we present an algorithm for, given a scheme, finding conserved quantities. We illustrate our algorithm by studying several finite-difference schemes.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/676654 |
| Date | 04 1900 |
| Creators | Krannich, Friedemann |
| Contributors | Gomes, Diogo A., Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Schmid, Peter, Parsani, Matteo |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | 2023-04-27, At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis will become available to the public after the expiration of the embargo on 2023-04-27. |
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