Geometric integrator

Summary

A geometric integrator is a numerical method for differential equations that keeps exactly a geometric property of the exact flow. Examples of such properties are symplecticity, a conserved quantity, volume, time-reversibility, and staying on a manifold. General-purpose methods only approximate such properties, and the small violations add up over long times. Keeping the structure exactly gives much better qualitative behaviour in long simulations, for example in celestial mechanics and molecular dynamics. Symplectic integrators are the best known class.