Abstract
The two previous papers of this series [1,2] qualitatively clarified the main function of symplectic algorithm [3–6] of maintaining the global structure of hamiltonian systems. In this paper we exploit one of its quantitative advantages—the control of rapid growth of along-track error. With a small improvement in the explicit symplectic difference scheme for separable systems, the algorithm can be extended to more general systems containing small dissipative and non-separable terms. Very good results were obtained showing that the symplectic algorithm has great advantages over usual, non-symplectic ones.
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