The topic of geometric integrators, i.e., numerical methods for differential equations that preserve important qualitative features of the system, has attracted much interest in recent years. The first class of systems for which such methods were derived are Hamiltonian systems. Here symplectic integrators preserve the symplectic structure of the phase space and are known to possess superior stability properties, in particular for long time computations. This makes them very popular for applications in celestial mechanics and molecular dynamics.

----Werner M. Seiler