  The largest contributions to the $n=2$ Lamb-shift, fine structure interval
and $2s$ hyperfine structure of muonic hydrogen are calculated by exact
numerical evaluations of the Dirac equation, rather than by a perturbation
expansion in powers of $1/c$, in the framework of non-relativistic quantum
electrodynamics. Previous calculations and the validity of the perturbation
expansion for light elements are confirmed. The dependence of the various
effects on the nuclear size and model are studied
