One class of conservative difference schemes for solving molecular   dynamics equations of motion
  Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of calculations. An approach for constructing symmetric simplectic numerical schemes with given approximation accuracy in relation to integration step, for solving molecular dynamics Hamiltonian equations, is proposed in this paper. Numerical experiments show that obtained under this approach symmetric simplectic third order scheme is more stable for integration step, time-reversible and conserves Hamiltonian of the system with more accuracy at a large integration interval then second order velocity Verlet numerical schemes. 
Eduard G. Nikonov
math.NA