Exponential Lawson methods are well known to have a severe order reduction when integrating stiff
problems. In a previous article, the precise order observed with Lawson methods when integrating linear
problems is justified in terms of different conditions of annihilation on the boundary. In fact, the analysis
of convergence with all exponential methods when applied to parabolic problems has always been performed
under assumptions of vanishing boundary conditions for the solution. In this article, we offer a
generalization of Lawson methods to approximate problems with nonvanishing and even time-dependent
boundary values. This technique is cheap and allows to avoid completely order reduction independently
of having vanishing or nonvanishing boundary conditions.
