标题：The Conservative Splitting High-Order Compact Finite Difference Scheme for Two-Dimensional Schrödinger Equations
作者：Wang, Bo ;Liang, Dong ;Sun, Tongjun
作者机构：[Wang, Bo ;Sun, Tongjun ] School of Mathematics, Shandong University, Jinan, Shandong; 250100, China;[Liang, Dong ] Department of Mathematics and Stat 更多
来源：International Journal of Computational Methods
摘要：In this paper, a new conservative and splitting fourth-order compact difference scheme is proposed and analyzed for solving two-dimensional linear Schrödinger equations. The proposed splitting high-order compact scheme in two dimensions has the excellent property that it preserves the conservations of charge and energy. We strictly prove that the scheme satisfies the charge and energy conservations and it is unconditionally stable. We also prove the optimal error estimate of fourth-order accuracy in spatial step and second-order accuracy in time step. The scheme can be easily implemented and extended to higher dimensional problems. Numerical examples are presented to confirm our theoretical results.
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