A molecular dynamics model for symplectic integrators

Mechanical systems in the very large scale like in celestial mechanics or in the very small scale like in the molecular dynamics can be modelled without dissipation. The resulting Hamiltonian systems possess conservation properties, which are characterized with the term symplecticness. Numerical integration schemes should preserve the symplecticness. Different methods are introduced and their performance is studied for constant and variable step size. As test examples two systems from molecular dynamics are introduced.