Symplectic algebraic dynamics algorithm

Based on the algebraic dynamics solution of ordinary differential equations and integration of L, the symplectic algebraic dynamics algorithm sU(n), is designed, which preserves the local symplectic geometric structure of a Hamiltonian system and possesses the same precision of the naive algebraic dynamics algorithm U-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 sU(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.