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.
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.
出处
《漳州师范学院学报（自然科学版）》
2012年第1期26-34,共9页
Journal of ZhangZhou Teachers College（Natural Science)
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
linear Schrodinger equation
generalized finite-difference time.domain method （GFDTD）
compact finite difference scheme
