  For diffusion-reaction equations employing a splitting procedure is
attractive as it reduces the computational demand and facilitates a parallel
implementation. Moreover, it opens up the possibility to construct second-order
integrators that preserve positivity. However, for boundary conditions that are
neither periodic nor of homogeneous Dirichlet type order reduction limits its
usefulness. In the situation described the Strang splitting procedure is not
more accurate than Lie splitting. In this paper, we propose a splitting
procedure that, while retaining all the favorable properties of the original
method, does not suffer from order reduction. We demonstrate our results by
conducting numerical simulations in one and two space dimensions with
inhomogeneous and time dependent Dirichlet boundary conditions. In addition, a
mathematical rigorous convergence analysis is conducted that confirms the
results observed in the numerical simulations.
