Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
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DOI：
10.1016/j.apnum.2010.12.004
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发表时间：
2011-04
影响因子：
2.8
通讯作者：
Zhen Gao;Shusen Xie
中科院分区：
文献类型：
--
作者：
Zhen Gao;Shusen Xie
本文构造了求解二维薛定谔方程的交替方向隐式紧致差分格式。这些格式的收敛速度为O（h ~ 4 +τ ~ 2）阶。数值实验表明，这些格式保持了电荷和能量守恒定律，并达到了预期的收敛速度。有代表性的模拟表明，所提出的计划是适用于工程利益和竞争力的问题相比，其他现有的程序。
In this paper, alternating direction implicit compact finite difference schemes are devised for the numerical solution of two-dimensional Schrödinger equations. The convergence rates of the present schemes are of order O(h4+τ2). Numerical experiments show that these schemes preserve the conservation laws of charge and energy and achieve the expected convergence rates. Representative simulations show that the proposed schemes are applicable to problems of engineering interest and competitive when compared to other existing procedures.