It is well known the order reduction phenomenon which arises when
exponential methods are used to integrate in time 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 paper, a technique is suggested to avoid that
order reduction. We deal directly with non-homogeneous
time-dependent boundary conditions, without having to reduce the
problem to 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.
