Here are some notes on conservative time discretization methods for stiff Hamiltonian systems, with some applications to modeling and simulation of energy transfer along protein molecules. They are based on the slides for a talk that I gave at the Center for Scientific Computing and Mathematical Modeling at the University of Maryland, College Park on September 26, but with a few corrections, and with some items that I did not cover in the talk, to make these notes more comprehensive as background reading for students.
Conservative time-discretization for stiff Hamiltonian systems, and molecular chain models