标题：The finite difference scheme for nonlinear Schrödinger equations on unbounded domain by artificial boundary conditions
作者：Wang, Bo ;Liang, Dong
作者机构：[Wang, Bo ] School of Mathematics, Shandong University, Jinan; Shandong; 250100, China;[Liang, Dong ] School of Mathematical Sciences, Ocean Universit 更多
来源：Applied Numerical Mathematics
摘要：In this paper, we propose and analyze a finite difference method for the nonlinear Schrödinger equations on unbounded domain by using artificial boundary conditions. Two artificial boundary conditions are introduced to restrict the original Schrödinger equations on an unbounded domain into an initial–boundary value problem with a bounded domain. Then, a finite difference scheme for the reduced problem is proposed. The important feature of the proposed scheme is that an extrapolation operator is introduced to treat the nonlinear term while the scheme keeps unconditionally stable and does not introduce any oscillations at the artificial boundaries. The proposed scheme with the discrete artificial boundary conditions is rigorously analyzed to yield the unconditional stability and the scheme is also proved to be convergent. Numerical examples are given to show the performance of our scheme.
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