Comparison of efficiency among different techniques to avoid order reduction with Strang splitting

In this article, we offer a comparison in terms of computational efficiency between two techniques to avoid order reduction when using Strang method to integrate nonlinear initial boundary value problems with time-dependent boundary conditions. We see that it is important to consider an exponential method for the integration of the linear nonhomogeneous and stiff part in the technique by Einkemmer et al. so that the latter is comparable in efficiency with that suggested by Alonso et al. Some other advantages of the technique suggested by Alonso et al. are stated in the conclusions.