Structure-preserving algorithms for autonomous Birkhoffian systems

The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhoffian systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.