  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 and we approximate the action in
a small time step by the Simpson's quadrature formula. The resulting scheme is
explicited for an elementary harmonic oscillator. It is a stable, explicit, and
symplectic scheme satisfying the conservation of an approximate energy.
Numerical tests illustrate our theoretical study.
