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

Jiwei Zhang, Zhizhong Sun, Xiaonan Wu & Desheng Wang

DOI: 10.4208/cicp.280610.161110a

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

Published online: 2011-10

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  • Abstract

The paper is concerned with the numerical solution of Schrödinger 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.

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@Article{CiCP-10-742, author = {Jiwei Zhang, Zhizhong Sun, Xiaonan Wu and Desheng Wang}, title = {Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {3}, pages = {742--766}, abstract = {

The paper is concerned with the numerical solution of Schrödinger 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.280610.161110a}, url = {http://global-sci.org/intro/article_detail/cicp/7459.html} }
TY - JOUR T1 - Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation AU - Jiwei Zhang, Zhizhong Sun, Xiaonan Wu & Desheng Wang JO - Communications in Computational Physics VL - 3 SP - 742 EP - 766 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.280610.161110a UR - https://global-sci.org/intro/article_detail/cicp/7459.html KW - AB -

The paper is concerned with the numerical solution of Schrödinger 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.

Jiwei Zhang, Zhizhong Sun, Xiaonan Wu and Desheng Wang. (2011). Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation. Communications in Computational Physics. 10 (3). 742-766. doi:10.4208/cicp.280610.161110a
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