Relations among Lie formal series and construction of symplectic integrators

  • P. -V. Koseleff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 673)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • P. -V. Koseleff
    • 1
  1. 1.Aleph et Géode Centre de Mathématiques, École PolytechniquePalaiseau

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