Error analysis of variational integrators of unconstrained Lagrangian systems

Due to a singularity or degeneracy at zero time-step, existence and uniqueness, and accuracy, of variational integrators, cannot be established by straightforward use of the implicit function theorem. We show existence and uniqueness for variational integrators by blowing up the variational principle. The blow-up implies an accuracy one less than is observed in simulations, a deficit that is recovered by a past–future symmetry at zero time-step.