In this paper

a new solution to the three-stage third-order non-gradient symplectic integration algorithm is given based on the minimum phase error principle and the partitioned Runge-Kutta form.Several other non-gradient methods

such as Ruth’s

McLachlan&Atela’s and Iwatsu’s symplectic integration algorithm of three-stage third-order

are employed to compare the performance with the present algorithm by numerical experiments.The numerical results show that the present algorithm is good at stability

and much superior to the other methods in the features of long-time computing ability.The further numerical experiments is used to compare the algorithm with above non-gradient symplectic methods and some force-gradient symplectic methods

the results also show that the algorithm is effective with high accuracy.These appealing features of the algorithm would make it effective to have the ability of structure-preserving and long-time tracing.