Procedure for Constructing Simplectic Numerical Schemes for Solving of Hamiltonian Systems of Equations

Numerical schemes which is used for solving of many-particle dynamics systems of equations can have restrictions on a step and an interval of integration because if its increase the numerical schemes became unstable and don’t conserve existing integrals of motion. As a result when we simulate many-particle system behavior on the sufficiently large time interval we should decrease an integration step which leads to considerableincreasing of computation quantity. In this paper a new procedure for constructing simplectic numerical schemes for solving of Hamiltonian systems of equations is proposed. A method for symmetrization of received simplectics numerical schemes is proposed too. Constructed by proposed in the paper procedure numerical schemes conserve energy of a system on the large interval of numerical integration for relatively large integration step incomparison with Verlet method which is usually used for solving of equations of motion in molecular dynamics. Results of numerical experiments are given in the paper. These results show main advantages of received symmetric simplectic numerical schemes of third order of accuracy for the integration step for the Hamiltonian systems of equations in comparison with numerical schemes of Verlet method of second order of accuracy.

Hamiltonian systems of equations, simplectic difference schemes, generating functions, molecular dynamics