Conformal symplectic; structure preserving; linear stability
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.
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Master of Science (M.S.)
College of Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic
Floyd, Dwayne, "Comparison of Second Order Conformal Symplectic Schemes with Linear Stability Analysis" (2014). Electronic Theses and Dissertations. 668.