  We propose a variational symplectic numerical method for the time integration
of dynamical systems issued from the least action principle. We assume a
quadratic internal interpolation of the state between two time steps and we
approximate the action in one time step by the Simpson's quadrature formula.
The resulting scheme is nonlinear and symplectic. First numerical experiments
concern a nonlinear pendulum and we have observed experimentally very good
convergence properties.
