We develop computer-assisted methods of proof for rigorous computation of the Evans function in order to prove stability of traveling waves. We use the parameterization method, series solutions, and the Newton-Kantorovich Theorem to obtain precise, rigorous error bounds for the numerical solution of the ODE used in the construction of the Evans function. We demonstrate these methods on a scalar reaction-diffusion model and on the Gray-Scott model.
Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-11319 |
Date | 20 April 2023 |
Creators | McGhie, Devin |
Publisher | BYU ScholarsArchive |
Source Sets | Brigham Young University |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Theses and Dissertations |
Rights | https://lib.byu.edu/about/copyright/ |
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