You are here

Comparison of Second Order Conformal Symplectic Schemes with Linear Stability Analysis

Download pdf | Full Screen View

Date Issued:
2014
Abstract/Description:
Numerical methods for solving linearly damped Hamiltonian ordinary differential equations are analyzed and compared. The methods are constructed from the well-known St(&)#246;rmer-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 constantand 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.
Title: Comparison of Second Order Conformal Symplectic Schemes with Linear Stability Analysis.
19 views
11 downloads
Name(s): Floyd, Dwayne, Author
Moore, Brian, Committee Chair
Schober, Constance, Committee Member
Mohapatra, Ram, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2014
Publisher: University of Central Florida
Language(s): English
Abstract/Description: Numerical methods for solving linearly damped Hamiltonian ordinary differential equations are analyzed and compared. The methods are constructed from the well-known St(&)#246;rmer-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 constantand 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.
Identifier: CFE0005793 (IID), ucf:50051 (fedora)
Note(s): 2014-12-01
M.S.
Sciences, Mathematics
Masters
This record was generated from author submitted information.
Subject(s): conformal symplectic -- structure-preserving -- linear stability
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0005793
Restrictions on Access: public 2015-06-15
Host Institution: UCF

In Collections