Abstract

Differential equations are frequently used for modeling systems in the physical sciences, biology, and other important real-world disciplines. Oftentimes, however, these equations cannot be solved exactly, so suitable computer algorithms are necessary to provide an approximated solution. While these computational simulations fail to exactly represent all behaviors of the true solution, they can be constructed to exactly, or very closely, reproduce certain properties which are key to the physical or scientific applications of a problem. This paper explores a computational method specifically constructed for modeling the behavior of systems with linear damping, or a reduction of energy, introduced in them. The method was designed to be conformal symplectic, and closely reproduce dissipation of physical properties such as linear and angular momentum, mass, and energy, caused by the damping. The algorithm was constructed in such a way that it maintains low computational cost to implement. Additionally, the method demonstrates favorable accuracy and stability properties in simulation. The method can also handle more complex scenarios, such as systems with forcing terms, and nonlinear systems. In these cases, it has been shown to hold advantages over other commonly used methods in particular circumstances.

Thesis Completion

2023

Semester

Fall

Thesis Chair/Advisor

Moore, Brian

Co-Chair

Schober, Constance

Degree

Bachelor of Science (B.S.)

College

College of Sciences

Department

Mathematics

Language

English

Access Status

Campus Access

Length of Campus-only Access

3 years

Release Date

12-15-2023

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