  Discrete variational methods have shown an excellent performance in numerical
simulations of different mechanical systems. In this paper, we introduce an
iterative method for discrete variational methods appropriate for boundary
value problems. More concretely, we explore a parallelization strategy that
leverages the power of multicore CPUs and GPUs (graphics cards). We study this
parallel method for first-order and second-order Lagrangians and we illustrate
its excellent behavior in some interesting applications, namely Zermelo's
navigation problem, a fuel-optimal navigation problem, and an interpolation
problem.
