Numerische Mathematik

, Volume 137, Issue 4, pp 1001–1037 | Cite as

Modified equations for variational integrators

  • Mats VermeerenEmail author


It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamiltonian. We investigate this property from the variational side. We present a technique to construct a Lagrangian for the modified equation from the discrete Lagrangian of a variational integrator.

Mathematics Subject Classification

65L99 70H03 70H25 


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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Institut für Mathematik, MA 7-1Technische Universität BerlinBerlinGermany

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