Avoiding order reduction when integrating nonlinear Schrödinger equation with Strang method

Abstract

In this paper a technique is suggested to avoid order reduction when using Strang method to integrate nonlinear Schrödinger equation subject to time-dependent Dirichlet boundary conditions. The computational cost of this technique is negligible compared to that of the method itself, at least when the timestepsize is fixed. Moreover, a thorough error analysis is given as well as a modification of the technique which allows to conserve the symmetry of the method while retaining its second order.