It is well known the order reduction phenomenon which arises when exponential methods are used to
integrate time-dependent initial boundary value problems, so that the classical order of these methods is
reduced. In particular, this subject has been recently studied for Lie–Trotter and Strang exponential splitting
methods, and the order observed in practice has been exactly calculated. In this article, a technique is
suggested to avoid that order reduction. We deal directly with nonhomogeneous time-dependent boundary
conditions, without having to reduce the problem to the homogeneous ones. We give a thorough error
analysis of the full discretization and justify why the computational cost of the technique is negligible in
comparison with the rest of the calculations of the method. Some numerical results for dimension splittings
are shown, which corroborate that much more accuracy is achieved.
