| 解线性薛定谔方程的广义时域有限差分方法的紧致形式 |
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| 引用本文： | 晏云,戴伟忠.解线性薛定谔方程的广义时域有限差分方法的紧致形式[J].漳州师院学报,2012(1):26-34. |
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| 作者姓名： | 晏云 戴伟忠 |
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| 作者单位： | [1]漳州师范学院数学与信息科学系,福建漳州363000 [2]路易斯安那理工大学工程和科学学院,美国路易斯安那拉斯顿71272 |
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| 摘 要： | 文献1]提出了求解线性薛定谔方程的广义时域有限差分方法（GFDTD）,其中的Laplace算子是用二阶中心差分和四阶中心差分逼近的.本文用文献2]提出的一般的紧致差分格式来逼近Laplace算子,从而得到了紧致形式的广义时域有限差分方法（CGFDTD）.我们分析了其稳定性条件,数值算例结果证实了理论分析.
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| 关 键 词： | 线性薛定谔方程 广义时域有限差分方法（GFDTD） 紧致差分格式 |
Compact Form of a Generalized Finite-Difference Time-Domain Method for Solving a Linear Schrodinger Equation |
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| YAN Yun,DAI Wei-zhong.Compact Form of a Generalized Finite-Difference Time-Domain Method for Solving a Linear Schrodinger Equation[J].Journal of ZhangZhou Teachers College(Philosophy & Social Sciences),2012(1):26-34. |
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| Authors: | YAN Yun DAI Wei-zhong |
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| Institution: | 1.Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, Fujian 363000, China; 2.College of Engineering and Science, Louisiana Tech University, Rnston, LA71272, USA ) |
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| Abstract: | A generalized finite-difference time-domain method （GFDTD） for solving a linear Schr＇odinger equation was put forward in W. Dal and F.I. Moxley＇s paper, in which the Laplace operator was approximated respectively by a second-order central difference operator and a fourth-order central difference operator. In this paper, the compact finite difference scheme given by S.K. Lele is applied to approximate the Laplace operator, and the writers obtain the compact form of the generalized finite-difference time-domain method （CGFDTD）. Stability conditions of the CGFDTD scheme is analyzed in this paper and the numerical results coincide with the theoretical analysis. |
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| Keywords: | linear Schrodinger equation generalized finite-difference time domain method （GFDTD） compact finite difference scheme |
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