期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 225, 期 1, 页码 124-134出版社
ELSEVIER
DOI: 10.1016/j.cam.2008.07.008
关键词
Schrodinger equation; Compact finite difference scheme; Boundary value methods; High accuracy
In this paper, a high-order and accurate method is proposed for solving the unsteady two-dimensional Schrodinger equation. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivatives and a boundary value method Of fourth-order for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. Moreover this method is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are compared with analytical solutions and with those provided by other methods in the literature. These results show that the combination of a compact finite difference approximation of fourth-order and a fourth-order boundary value method gives an efficient algorithm for solving the two dimensional Schrodinger equation. (C) 2008 Elsevier B.V. All rights reserved.
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