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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 asymptoticexpansion for the solution with respect to the small parameter depending on theinverse of the square of the speed of light. As the first terms of thisasymptotic can easily be simulated our approach allows us to constructnumerical algorithms that are robust with respect to the large parameter cproducing high oscillations in the exact solution.

Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime