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On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. I. (English) Zbl 1119.65085

The authors present transparent boundary conditions for Crank-Nicolson discretizations of the Schrödinger equation in one and two dimensions. The analysis is performed using a discrete Laplace transform. An energy inequality is used to prove stability of the method.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q40 PDEs in connection with quantum mechanics
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A10 Laplace transform
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