  We investigate the muonic hydrogen 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2}
transition through a precise, non-perturbative numerical solution of the Dirac
equation including the finite-size Coulomb force and finite size vacuum
polarization. The results are compared with earlier perturbative calculations
of (primarily) Borie, Martynenko, and Pachucki; and experimental results
recently presented by Pohl et al., in which this very comparison is interpreted
as requiring a modification of the proton charge radius from that obtained in
electron scattering and electronic hydrogen analyses. We find no significant
discrepancy between the perturbative and non-perturbative calculations, and
present our results as confirmation of the perturbative methods.
