[1]符莉丹,孔令华,王兰,等.非齐次Schrdinger方程的交替隐式格式[J].江西师范大学学报(自然科学版),2014,(02):167-170.
 FU Li-dan,KONG Ling-hua,WANG Lan,et al.The Alternative Direction Implicit Scheme for Inhomogeneous Schr(o)dinger Equation[J].,2014,(02):167-170.
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非齐次Schrdinger方程的交替隐式格式()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年02期
页码:
167-170
栏目:
出版日期:
2014-04-30

文章信息/Info

Title:
The Alternative Direction Implicit Scheme for Inhomogeneous Schr(o)dinger Equation
作者:
符莉丹;孔令华;王兰;符芳芳;黄晓梅
江西师范大学数学与信息科学学院,江西南昌,330022;南昌工学院基础部,江西南昌,330108
Author(s):
FU Li-dan;KONG Ling-hua;WANG Lan;FU Fang-fang;HUANG Xiao-mei
关键词:
Schr(o)dinger方程交替方向法Taylor展开
Keywords:
Schr(o)dinger equationalternative direction implicit schemeTaylor's expansion
分类号:
O241.8
文献标志码:
A
摘要:
以Taylor展开为基本工具,研究了非齐次多维Schr(o)dinger方程的交替方向隐格式.此格式在时空方向均具有2阶精度,而且所需求解的代数方程组的阶数与1维问题一样,具有经济、实用、易于模块化编程实现等优点.数值实验主要检验了数值格式长时间的模拟能力、离散电荷随时间演化关系等.
Abstract:
Based on Taylor's expansion,an alternative direction implicit scheme was proposed for multidimensional Schrödinger equation.The scheme is of second order both in time and space.Moreover,the scale of the algebraic equations resulting from the scheme is the same with a one-dimensional problem.It is economic,practical and can be coded modularly.Numerical experiments verify the long-term simulation of the developed scheme to original problem and the evolution of discrete charge against time.

参考文献/References:

[1] Griffiths D J.Introduction to quantum mechanics [M].2nd. New Jersey:Pearson Prentice Hall,2005.
[2] 程明.若干Schrödinger方程及其应用 [D].长春:吉林大学,2013.
[3] 马院萍,孔令华,王兰.2维Schrödinger方程的高阶紧致ADI格式 [J].江西师范大学学报:自然科学版,2010,34(4):421-425.
[4] Liao Honglin,Sun Zhizhong,Shi Hansheng.Error estimate of fourth-order compact scheme for linear Schrödinger equations [J].SIAM J Numerical Analysis,2010,47(6):4381-4401.
[5] Chang Qianshun,Jia E,Sun W.Difference schemes for solving the generalized nonlinear Schrödinger equation [J].J Comput Phys,1999,148(2):397-415.
[6] Liao Honglin,Sun Zhizhong.Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations [J].Numer Methods PDEs,2010,26(1):37-60.
[7] 符芳芳,孔令华,王兰,等.一类新的含双幂非线性项的Schrödinger方程的差分式 [J].江西师范大学学报:自然科学版,2010,34(1):22-26.
[8] 陆金甫,关治.偏微分方程数值解法 [M].北京:清华大学出版社,2004.
[9] 张鲁明.非线性Schrödinger方程的高精度守恒差分格式 [J].应用数学学报,2005,28(1):178-186.
[10] Hong Jialin,Liu Ying,Munthe-Kaas H,et al.Globally conservative properties and error estimation of a multisymplectic scheme for Schrödinger equations with variable coefficients [J].Appl Numer Math,2006,56(6):814-843.
[11] Kong Linghua,Hong Jialin,Wang Lan,et al.Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term [J].J Comput Appl Math,2009,231(2):664-678.
[12] 王兰.多辛Preissman格式及其应用 [J].江西师范大学学报:自然科学版,2009,33(1):42-46.
[13] 黄红,王兰.薛定谔方程的局部1维多辛格式 [J].江西师范大学学报:自然科学版,2011,35(5):455-458.
[14] Peaceman D,Rachford H.The numerical solution of parabolic and elliptic equations [J].J Soc Indust Appl Math,1955,3(1):28-41.
[15] Kong Linghua,Hong Jialin,Zhang Jingjing.Splitting multisymplectic integrators for Maxwell's equations [J].J Comput Phys,2010,229(11):4259-4278.
[16] Dai Weizhong,Nassar R.Compact ADI method for solving parabolic differential equations [J].Numer Methods PDEs,2002,18(2):129-142.
[17] Li Jichun,Chen Yitung,Liu Guoqing.High-order compact ADI methods for parabolic equations [J].Comput Math with Application,2006,52(8/9):1343-1356.
[18] Kong Linghua,Duan Yali,Wang Lan,et al.Spectral-like resolution compact ADI finite difference method for the multi-dimensional Schrödinger equations [J].Math Comput Model,2012,55(8/9):1798-1812.
[19] 张星,单双荣. 高维抛物型方程的一个高精度恒稳定的交替方向格式 [J].工程数学学报,2011,28(1):61-66.
[20] 尹丽萍.薛定谔方程的高精度差分格式及紧交替方向格式[D].青岛:中国海洋大学,2009.
[21] 邓定文.高精度交替方向隐式差分法的理论与应用 [D].武汉:华中科技大学,2012.
[22] 李雪玲,孙志忠. 二维变系数反应扩散方程的紧交替方向差分格式 [J]. 高等学校计算数学学报,2006,28(1):83-95.
[23] 吴宏伟.二维半线性反应扩散方程的交替方向隐格式 [J].计算数学,2008,30(4):349-360.
[24] 魏剑英.求解二维热传导方程的高精度紧致差分方法 [J].西南师范大学学报:自然科学版,2013,38(12):50-54.

备注/Memo

备注/Memo:
国家自然科学基金(11211171,11301234);江西省自然科学基金(20114BAB201011);江西省教育厅基金(GJJ12174)
更新日期/Last Update: 1900-01-01