The explicit integration is based on a multi-stage Runge-Kutta scheme. In this case the Courant number is typically limited to one, although under certain circumstances, values of up to two may remain stable. This restriction is much more severe than the implicit integration scheme, although much less storage will be required for the same size problem.
Residual smoothing can be employed along with the explicit integration scheme to help widen the stability margin and allow slightly larger Courant numbers to be used.