Conservative Integrators for Many-body Problems

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.

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