Date of Award
Master of Science - Mathematical Sciences
Mathematics and Statistics
Matthew A. Beauregard
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.
Weymier, Emily Jean, "Theoretical Analysis of Nonlinear Differential Equations" (2018). Electronic Theses and Dissertations. 145.
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