Volume 10, Issue 3
Analysis of High-order Absorbing Boundary Conditions for the Schrödinger Equation

Jiwei Zhang ,  Zhizhong Sun ,  Xiaonan Wu and Desheng Wang

10.4208/cicp.280610.161110a

Commun. Comput. Phys., 10 (2011), pp. 742-766.

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  • Abstract

The paper is concerned with the numerical solution of Schr ¨odinger equations on an unbounded spatial domain. High-order absorbing boundary conditions for one-dimensional domain are derived, and the stability of the reduced initial boundary value problem in the computational interval is proved by energy estimate. Then a second order finite difference scheme is proposed, and the convergence of the scheme is established as well. Finally, numerical examples are reported to confirm our error estimates of the numerical methods.

  • History

Published online: 2011-10

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