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A symplectic integration algorithm for separable Hamiltonian functions. (English) Zbl 0709.70012
Summary: 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.

MSC:
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
70H05 Hamilton’s equations
70-08 Computational methods for problems pertaining to mechanics of particles and systems
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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