Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations

详细信息    查看全文

• 作者：Zhen Gao^a ; ^{zhengao.ouc@gmail.com} ; Shusen Xie^b ; ¹ ; ^{shusenxie@ouc.edu.cn}
• 关键词：Schr&#xf6 ; dinger equation ; ADI compact difference scheme ; Conservation law ; Error estimate
• 刊名：Applied Numerical Mathematics
• 出版年：2011
• 出版时间：April 2011
• 年：2011
• 卷：61
• 期：4
• 页码：593-614
• 全文大小：2007 K

文摘

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.