Symplectic algebraic dynamics algorithm

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.