Week 8: Paper Presentations and Final Project Pitches

Final Project Idea

Energy drift – usually damping – is substantial for numerical integration schemes that are not symplectic, such as the Runge-Kutta family.

Symplectic integrators usually used in molecular dynamics, such as the Verlet integrator family, exhibit increases in energy over very long time scales, though the error remains roughly constant. These integrators do not in fact reproduce the actual Hamiltonian mechanics of the system; instead, they reproduce a closely related “shadow” Hamiltonian whose value they conserve many orders of magnitude more closely.