Efficient time integration of the Maxwell-Klein-Gordon equation in the non-relativistic limit regime

The idea to overcome this numerical challenge is to filter out the high frequencies explicitly by asymptotically expanding the exact solution with respect to the small parameter c−2. This allows us to reduce the highly-oscillatory problem to its corresponding non-oscillatory Schrödinger-Poisson limit system. On the basis of this expansion we are then able to construct efficient numerical time integration schemes, which do NOT suffer from any c-dependent time step restriction.