  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.
