  Super-resolution of the Lie-Trotter splitting ($S_1$) and Strang splitting
($S_2$) is rigorously analyzed for the nonlinear Dirac equation without
external magnetic potentials in the nonrelativistic regime with a small
parameter $0<\varepsilon\leq 1$ inversely proportional to the speed of light.
In this regime, the solution highly oscillates in time with wavelength at
$O(\varepsilon^2)$. The splitting methods surprisingly show super-resolution,
i.e. the methods can capture the solution accurately even if the time step size
$\tau$ is much larger than the sampled wavelength at $O(\varepsilon^2)$.
Similar to the linear case, $S_1$ and $S_2$ both exhibit $1/2$ order
convergence uniformly with respect to $\varepsilon$. Moreover, if $\tau$ is
non-resonant, i.e. $\tau$ is away from certain region determined by
$\varepsilon$, $S_1$ would yield an improved uniform first order $O(\tau)$
error bound, while $S_2$ would give improved uniform $3/2$ order convergence.
Numerical results are reported to confirm these rigorous results. Furthermore,
we note that super-resolution is still valid for higher order splitting
methods.
