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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