Date of Award


Degree Type


Degree Name

Master of Science - Mathematical Sciences


Mathematics and Statistics

First Advisor

Matthew A. Beauregard

Second Advisor

William Clark

Third Advisor

Thomas Judson

Fourth Advisor

Ryan Phelps


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.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.



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