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Zbl 1229.81011
Xie, Shusen; Li, Guangxing; Yi, Sucheol
Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation.
(English)
[J] Comput. Methods Appl. Mech. Eng. 198, No. 9-12, 1052-1060 (2009). ISSN 0045-7825

Summary: In this paper, two compact finite difference schemes are presented for the numerical solution of the one-dimensional nonlinear Schrödinger equation. The discrete $L_{2}$-norm error estimates show that convergence rates of the present schemes are of order $O(h^{4}+\tau ^{2})$. Numerical experiments on some model problems show that the present schemes preserve the conservation laws of charge and energy and are of high accuracy.
MSC 2000:
*81-08 Computational methods (quantum theory)
81Q05 Closed and approximate solutions to quantum-mechanical equations

Keywords: nonlinear Schrödinger equation; compact finite difference scheme; conservation law; error estimate; soliton

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