Solvable Map Method for Integrating Nonlinear Hamiltonian Systems

Abstract

Conventional numerical integration algorithms can not be used for long term stability studies of complicated nonlinear Hamiltonian systems since they do not preserve the symplectic structure of the system. Further, they can be very slow even if supercomputers are used. In this paper, we study the symplectic integration algorithm using solvable maps which is both fast and accurate and extend it to six dimensions. This extension enables single particle studies using all three degrees of freedom.