  The Strang splitting method, formally of order two, can suffer from order
reduction when applied to semilinear parabolic problems with inhomogeneous
boundary conditions. The recent work [L .Einkemmer and A. Ostermann. Overcoming
order reduction in diffusion-reaction splitting. Part 1. Dirichlet boundary
conditions. SIAM J. Sci. Comput., 37, 2015. Part 2: Oblique boundary
conditions, SIAM J. Sci. Comput., 38, 2016] introduces a modification of the
method to avoid the reduction of order based on the nonlinearity. In this paper
we introduce a new correction constructed directly from the flow of the
nonlinearity and which requires no evaluation of the source term or its
derivatives. The goal is twofold. One, this new modification requires only one
evaluation of the diffusion flow and one evaluation of the source term flow at
each step of the algorithm and it reduces the computational effort to construct
the correction. Second, numerical experiments suggest it is well suited in the
case where the nonlinearity is stiff. We provide a convergence analysis of the
method for a smooth nonlinearity and perform numerical experiments to
illustrate the performances of the new approach.
