2008•arXiv (Cornell University)Open access

Error analysis of variational integrators of unconstrained Lagrangian systems

George W. Patrick, Charles Cuell

Abstract

A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future symmetry.

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Key concepts: Variational integrator, Lagrangian, Integrator, Variational analysis, Applied mathematics, Error analysis, Mathematics, Computer science