Avoiding order reduction when integrating linear initial boundary value problems with exponential splitting methods

Abstract

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.