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

Abstract

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.