Comparison of split step solvers for multidimensional Schrödinger problems

Abstract

This paper presents the analysis of the split step solvers for multidimensional Schrödinger problems. The second-order symmetrical splitting techniques are applied. The standard operator splitting is used to split the linear diffraction and reaction/potential processes. The dimension splitting exploits the commuting property of one-dimensional discrete diffraction operators. Alternating Direction Implicit (ADI) and Locally One-Dimensional (LOD) algorithms are constructed and stability is investigated for two- and three-dimensional problems. Compact high-order approximations are applied to discretize diffraction operators. Results of numerical experiments are presented and convergence of finite difference schemes is investigated.