Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrodinger equation

A general method is proposed to build exact artificial boundary conditions for the one-dimensional nonlocal Schrodinger equation. To this end, we first consider the spatial semi-discretization of the nonlocal equation, and then develop an accurate numerical method for computing the Green's function of the semi-discrete nonlocal Schrodinger equation. These Green's functions are next used to build the exact boundary conditions corresponding to the semi-discrete model. Numerical results illustrate the accuracy of the boundary conditions. The methodology can also be applied to other nonlocal models and could be extended to higher dimensions. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The proposed method presents a general approach to construct exact artificial boundary conditions for the one-dimensional nonlocal Schrodinger equation by semi-discretizing the equation spatially and developing an accurate numerical method for computing the Green's function. The numerical results demonstrate the accuracy of the boundary conditions and the potential application of the method to other nonlocal models and higher dimensions.