Keywords

Conformal symplectic; structure preserving; linear stability

Abstract

Numerical methods for solving linearly damped Hamiltonian ordinary differential equations are analyzed and compared. The methods are constructed from the well-known Störmer-Verlet and implicit midpoint methods. The structure preservation properties of each method are shown analytically and numerically. Each method is shown to preserve a symplectic form up to a constant and are therefore conformal symplectic integrators, with each method shown to accurately preserve the rate of momentum dissipation. An analytical linear stability analysis is completed for each method, establishing thresholds between the value of the damping coefficient and the step-size that ensure stability. The methods are all second order and the preservation of the rate of energy dissipation is compared to that of a third order Runge-Kutta method that does not preserve conformal properties. Numerical experiments will include the damped harmonic oscillator and the damped nonlinear pendulum.

Notes

If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu

Graduation Date

2014

Semester

Fall

Advisor

Moore, Brian

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Sciences

Format

application/pdf

Identifier

CFE0005793

URL

http://purl.fcla.edu/fcla/etd/CFE0005793

Language

English

Release Date

June 2015

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

Subjects

Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic

Download

Included in

Mathematics Commons

Share

COinS