Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation. (Q1399628)

The paper deals with the problem of constructing stable approximation schemes for the one-dimensional linear Schrödinger equation set in an unbounded domain. Futhermore some unconditionally stable discretization schemes are developed for the initial-boundary value problem in a bounded domain with a transparent boundary condition. The authors address two possible choices of transparent boundary conditions based on the Dirichlet-Neumann and Neumann-Dirichlet operators. Some numerical experiments are presented.