  We show that the Strang splitting method applied to a diffusion-reaction
equation with inhomogeneous general oblique boundary conditions is of order two
when the diffusion equation is solved with the Crank-Nicolson method, while
order reduction occurs in general if using other Runge-Kutta schemes or even
the exact flow itself for the diffusion part. We prove these results when the
source term only depends on the space variable, an assumption which makes the
splitting scheme equivalent to the Crank-Nicolson method itself applied to the
whole problem. Numerical experiments suggest that the second order convergence
persists with general nonlinearities.
