A SYMPLECTIC INTEGRATION ALGORITHM FOR SEPARABLE HAMILTONIAN FUNCTIONS

We derive an algorithm to numerically integrate differential equations derivable from a separable Hamiltonian function. This symplectic algorithm is accurate to fourth order in the time step and preserves exactly the Poincaré-Cartan integral invariants associated with the topology of the phase flow. We compare the efficiency and accuracy of this method to that of existing integrators (both symplectic and non-symplectic) by integrating the equations of motion corresponding to a nonlinear pendulum, a particle in the field of a standing wave, and a harmonic oscillator perturbed by a plane wave. © 1991.