Conservative symmetric second-order one-step schemes are derived for dynamical systems describing various many-body systems using the Discrete Multiplier Method. This includes conservative schemes for the $n$-species Lotka-Volterra system, the $n$-body problem with radially symmetric potential and the $n$-point vortex models in the plane and on the sphere. In particular, we recover Greenspan-Labudde's conservative schemes for the $n$-body problem. Numerical experiments are shown verifying the conservative property of the schemes and second-order accuracy.

翻译：保守的对称二阶一步方案是针对使用分辨倍增法描述多种机体系统的动态系统制定的,其中包括对以美元为单位的Lotka-Volterra系统的保守方案、对称潜力的辐射性对称型的美元-体问题以及飞机和球体上的美元-点旋涡模型。特别是,我们恢复了格林斯潘-拉布德对以美元为单位的保守方案。进行了数字实验,以核实方案的保守性能和第二阶的准确性。