Abstract
Based on the algebraic dynamics solution of ordinary differential equations and integration of \(\hat L\), the symplectic algebraic dynamics algorithm sÛ n is designed, which preserves the local symplectic geometric structure of a Hamiltonian system and possesses the same precision of the naïve algebraic dynamics algorithm Û n . Computer experiments for the 4th order algorithms are made for five test models and the numerical results are compared with the conventional symplectic geometric algorithm, indicating that sÛ n has higher precision, the algorithm-induced phase shift of the conventional symplectic geometric algorithm can be reduced, and the dynamical fidelity can be improved by one order of magnitude.
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