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

Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity