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

Pang, Gang; Yang, Yibo; Antoine, Xavier; Tang, Shaoqiang

doi:10.1090/mcom/3679

Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain
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by Gang Pang, Yibo Yang, Xavier Antoine and Shaoqiang Tang;

Math. Comp. 90 (2021), 2731-2756

DOI: https://doi.org/10.1090/mcom/3679

Published electronically: July 30, 2021

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Abstract:

Based on the semi-discrete artificial boundary condition introduced by Ji, Yang, and Antoine [Comput. Phys. Commun. 222 (2018), pp. 84–93] for the two-dimensional 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 $L^{2}$-stable and that the accuracy is second-order in time, confirming then the numerical results reported by Ji et al. (2018).

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