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Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>A general method is proposed forc constructing accurate artificial boundary conditions for the two-dimensional nonlocal Schr\u00f6dinger equation (where the derivative term [Formula: see text] is replaced by the fractional derivative [Formula: see text] with [Formula: see text]). A numerical algorithm is developed for computing the Green\u2019s functions of the fully discretized nonlocal Schr\u00f6dinger equation by a recursive relationship. The discrete Green\u2019s functions are used to construct the exact Dirichlet-to-Dirichlet-type boundary for the fully discretized nonlocal Schr\u00f6dinger equation. The numerical stability is proven, and numerical examples are provided to demonstrate the validity of the boundary conditions. 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