Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions

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