A Symplectic Integration Algorithm for Separable Hamiltonian Functions
Abstract
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 PoincaréCartan 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 nonsymplectic) 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 January 1991
 DOI:
 10.1016/00219991(91)90299Z
 Bibcode:
 1991JCoPh..92..230C