Relations Among Lie Formal Series and Construction of Symplectic Integrators

Symplectic integrators are numerical integration schemes for hamiltonian systems. The integration step is an explicit symplectic map. We find symplectic integrators using universal exponential identities or relations among formal Lie series. We give here general methods to compute such identities in a free Lie algebra. We recover by these methods all the previously known symplectic integrators and some new ones. We list all possible solutions for integrators of low order.

• Type: Conference
• Year: 1993
• Where: AAECC
• Authors: Pierre-Vincent Koseleff
• Keywords: AAECC 1993, Algorithms, Explicit Symplectic Map, Numerical Integration Schemes, Symplectic Integrators