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Analysis of High-Order Absorbing Boundary Conditions for the Schrödinger Equation

Published online by Cambridge University Press:  20 August 2015

Jiwei Zhang ,
Zhizhong Sun ,
Xiaonan Wu  and
Desheng Wang
Jiwei Zhang*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
Zhizhong Sun*
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, China
Xiaonan Wu*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong
Desheng Wang*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
*
Email:jzhang@cims.nyu.edu
Email:zzsun@seu.edu.cn
Corresponding author.Email:xwu@math.hkbu.edu.hk
Email:Desheng@ntu.edu.sg
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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.

Keywords

65M1265M0665M15Schrödinger equationfinite difference methodhigh-order absorbing boundary conditionconvergence
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 3 , September 2011 , pp. 742 - 766
Copyright
Copyright © Global Science Press Limited 2011

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