Date of Award
2-2018
Degree Type
Thesis
Degree Name
Master of Science - Mathematical Sciences
Department
Mathematics and Statistics
First Advisor
Matthew A. Beauregard
Second Advisor
William Clark
Third Advisor
Thomas Judson
Fourth Advisor
Ryan Phelps
Abstract
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, or lack thereof, of each technique. These techniques are integral in applied mathematics and it is shown that correct employment allows us to see the behavior of a differential equation when the exact solution may not be attainable.
Repository Citation
Weymier, Emily Jean, "Theoretical Analysis of Nonlinear Differential Equations" (2018). Electronic Theses and Dissertations. 145.
https://scholarworks.sfasu.edu/etds/145
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Included in
Analysis Commons, Non-linear Dynamics Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Mathematics Commons
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