Uniformly accurate integrators for Klein-Gordon-Schr\"odinger systems from the classical to non-relativistic limit regime

In this paper we present a novel class of asymptotic consistent exponential-type integrators for Klein-Gordon-Schr"odinger systems that capture all regimes from the slowly varying classical regime up to the highly oscillatory non-relativistic limit regime. We achieve convergence of order one and two that is uniform in $c$ without any time step size restrictions. In particular, we establish an explicit relation between gain in negative powers of the potentially large parameter $c$ in the error constant and loss in derivative.