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

Ducomet, B.; Zlotnik, A.

Commun. Math. Sci. 4, No. 4, 741-766 (2006).

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.

Reviewer: Gerald W. Hedstrom (Pleasanton)

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

Keywords:

transparent boundary condition; Schrödinger equation; Crank-Nicolson method; Laplace transform; stability