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

Gang Pang (1) , Yibo Yang (2) , Xavier Antoine (3, 4) , Shaoqiang Tang (5)

1 BUAA - Beijing University of Aeronautics and Astronautics
2 University of Pennsylvania
3 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
4 IECL - Institut Élie Cartan de Lorraine
5 Peking University [Beijing]

Based on the semi-discrete artificial boundary condition introduced in [24] for the twodimensional free Schrödinger equation in a computational rectangular domain, we propose to analyze the stability and convergence rate with respect to time of the resulting full scheme. We prove that the global scheme is L2-stable and that the accuracy is second-order in time, confirming then the numerical results reported in "Ji S., Yang Y., Pang G., Antoine X., Computer Physics Communications, 2018" [24].

Mots clés: convergence analysis; artificial boundary condition; stability analysis; Schrödinger equation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Gang Pang, Yibo Yang, Xavier Antoine, Shaoqiang Tang. Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain. Mathematics of Computation, 2021, 90 (332), pp.2731-2756. ⟨10.1090/mcom/3679⟩. ⟨hal-02340837v2⟩