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Journal Articles Mathematics of Computation Year : 2021

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

Abstract

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].
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Dates and versions

hal-02340837 , version 1 (31-10-2019)
hal-02340837 , version 2 (12-06-2021)

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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⟩
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