  We consider the Klein-Gordon equation in the non-relativistic limit regime,
i.e. the speed of light c tending to infinity. We construct an asymptotic
expansion for the solution with respect to the small parameter depending on the
inverse of the square of the speed of light. As the first terms of this
asymptotic can easily be simulated our approach allows us to construct
numerical algorithms that are robust with respect to the large parameter c
producing high oscillations in the exact solution.
