Dissertation
OPERATOR SPLITTING METHOD AND PROPAGATION FAILURE IN REACTION-DIFFUSION EQUATIONS
Washington State University
Doctor of Philosophy (PhD), Washington State University
05/2024
DOI:
https://doi.org/10.7273/000006529
Abstract
The focus of this dissertation is to study the solution behavior of the Nagumo type reaction-diffusion equation that is known for modeling impulse propagation in nerve axons. The study involves working with an operator splitting scheme along with an innovative regularization idea. The use of an operator splitting scheme helps in de-constructing a problem into simpler subproblems. Our work involves studying the the forward and inverse problems of the Nagumo equation. We also extend our study to understand pinning or propagation failure in the discrete version of the Nagumo equation. We implement the numerical scheme while maintaining the stability and accuracy of the full problem.
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Details
- Title
- OPERATOR SPLITTING METHOD AND PROPAGATION FAILURE IN REACTION-DIFFUSION EQUATIONS
- Creators
- Sharon-Yasotha K Veerayah-McGregor
- Contributors
- Valipuram S Manoranjan (Chair) - Washington State University, Mathematics and Statistics, Department ofAlexander Khapalov (Committee Member)Sergey Lapin (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 75
- Identifiers
- 99901121130801842
- Language
- English
- Resource Type
- Dissertation