A comparison of boundary correction methods for Strang splitting
For researchers using splitting methods with non-homogeneous boundary conditions, this provides a comparison and extension of existing corrections, but the results are incremental.
This paper compares two boundary correction methods for Strang splitting in the presence of non-homogeneous boundary conditions, extends one method to nonlinear problems with rigorous convergence analysis, and introduces a third-order extension. Numerical tests on diffusion-reaction, advection-reaction, and dispersion-reaction equations show relative performance.
In this paper we consider splitting methods in the presence of non-homogeneous boundary conditions. In particular, we consider the corrections that have been described and analyzed in Einkemmer, Ostermann 2015 and Alonso-Mallo, Cano, Reguera 2016. The latter method is extended to the non-linear case, and a rigorous convergence analysis is provided. We perform numerical simulations for diffusion-reaction, advection-reaction, and dispersion-reaction equations in order to evaluate the relative performance of these two corrections. Furthermore, we introduce an extension of both methods to obtain order three locally and evaluate under what circumstances this is beneficial.