Theoretical Analysis of Nonlinear Differential Equations

<p>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.</p>

Name thesis:degree_name

Master of Science - Mathematical Sciences

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics and Statistics

Year dc:date.available

2018

Author dc:creator

• Weymier, Emily Jean

Contributors dc:contributor

• Matthew A. Beauregard
• William Clark
• Thomas Judson

• differential equations
• analysis
• solution
• eigenvalue
• nonlinear equation
• Non-linear Dynamics
• Numerical Analysis and Computation
• Ordinary Differential Equations and Applied Dynamics
• Other Mathematics

Repository record dc:identifier

https://scholarworks.sfasu.edu/etds/145

OAI identifier oai:identifier

oai:scholarworks.sfasu.edu:etds-1157