Keywords
numerical methods; numerical analysis; scientific computing
Abstract
Planetary orbits, pendulums, and hurricanes are everyday examples of nonlinear systems, often studied using differential equations. However, their exact solutions can not always be computed, and thus, we use numerical methods to approximate their solutions. Certain methods are better suited to preserve special properties of the system like energy and geometry. Through previous numerical simulations, a conformal symplectic method proves more effective in this preservation. To understand why, we find the modified equation of a nonlinear system with damping, which is a differential equation for which the numerical solution is exact. Through backward error analysis, we obtain these modified equations, which reveal how well a method maintains these characteristics, along with its stability. Furthermore, numerical simulations are used to verify the error of the method and explore long-term behavior.
Thesis Completion Year
2025
Thesis Completion Semester
Spring
Thesis Chair
Moore, Brian
College
College of Sciences
Department
Mathematics
Thesis Discipline
Mathematics
Language
English
Access Status
Open Access
Length of Campus Access
None
Campus Location
Orlando (Main) Campus
STARS Citation
Keesler, Taylore M., "Modified Equations of Conformal Symplectic Exponential Time Differencing Methods" (2025). Honors Undergraduate Theses. 272.
https://stars.library.ucf.edu/hut2024/272
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