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

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

Jiwei Zhang 1, Zhizhong Sun 2, Xiaonan Wu 3*, Desheng Wang 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore.
2 Department of Mathematics, Southeast University, Nanjing 210096, China.
3 Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong.

Received 28 June 2010; Accepted (in revised version) 16 November 2010
Available online 1 June 2011


The paper is concerned with the numerical solution of Schrodinger 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.

AMS subject classifications: 65M12, 65M06, 65M15

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Key words: Schrodinger equation, finite difference method, high-order absorbing boundary condition, convergence.

*Corresponding author.
Email: (J. Zhang), (Z. Sun), (X. Wu), (D. Wang)

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