Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain

Abstract

Based on the discrete artificial boundary condition introduced in [23] for the two-dimensional free Schrodinger equation in a computational rectangular domain, we propose to analyze the stability and convergence rate of the resulting full scheme. We prove that the global scheme is L 2-stable and that the accuracy is second-order in time, confirming then the numerical results reported in [23].