How to avoid order reduction when Lawson methods integrate nonlinear initial boundary value problems

Abstract

It is well known that Lawson methods suffer from a severe order reduction when integrating initial boundary value problems where the solutions are not periodic in space or do not satisfy enough conditions of annihilation on the boundary. However, in a previous paper, a modification of Lawson quadrature rules has been suggested so that no order reduction turns up when integrating linear problems subject to timedependent boundary conditions. In this paper, we describe and thoroughly analyse a technique to avoid also order reduction when integrating nonlinear problems. This is very useful because, given any Runge–Kutta method of any classical order, a Lawson method can be constructed associated to it for which the order is conserved.