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The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions. (English) Zbl 1094.65088
The authors analyze a difference scheme for a one-dimensional Schrödinger equation with nonreflecting boundary condition. It is required that the potential term be constant outside a compact interval. An energy method is used to prove stability of the method and to estimate its rate of convergence.

65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
35Q40PDEs in connection with quantum mechanics
Full Text: DOI
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