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By solving the two-body Schordinger equation in a very high precisenonperturbative numerical (NPnum) way, we reexamine the contributions of fine,hyperfine structure splittings of muonic hydrogen based on the Breit potential.The comparison of our results with those by the first order perturbative theory($^{1st}$PT) in the literature shows, when the structure of proton isconsidered, the differences between the results by the $^{1st}$PT and NPnummethods are small for the fine and hyperfine splitting of $2P$ state, while areabout $-0.009$ meV and $0.08$ meV for the $F=1$ and total hyperfine splittingof $2S$ state of muonic hydrogen, respectively. These differences are largerthan the current experimental precision and would be significant to beconsidered in the theoretical calculation.

Nonperturbative numerical calculation of the fine and hyperfine  structure of muonic hydrogen by Breit potential including the effects from  the proton size