Dissertation
Fractional Operators and Variations Applied to Stefan Problems
Washington State University
Doctor of Philosophy (PhD), Washington State University
2023
DOI:
https://doi.org/10.7273/000006291
Abstract
In this thesis, we present a model for the free boundary Stefan problem. We begin with outlining the problem and its complexities, motivating the need for a numerical method. Then we introduce fractional operators, exploring various characteristics to narrow down the proper operator that will apply to the Stefan problem. We then outline our model, using the Caputo fractional derivative with a finite difference discretization and the SOR method to solve numerically. Our results are presented for different parameters such as latent heat and temperature. We end with suggestions for further work on our model.
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Details
- Title
- Fractional Operators and Variations Applied to Stefan Problems
- Creators
- Katrina Sabochick
- Contributors
- Sergey Lapin (Advisor)Lynn Schreyer (Committee Member)Daryl DeFord (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 79
- Identifiers
- 99901086433001842
- Language
- English
- Resource Type
- Dissertation