Schrdinger方程的紧致修正交替方向格式  

The Compact and Modified ADI Scheme for Schrdinger Equations

作　　者：王兰[1] 周媛兰[1] 符莉丹 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2016年第5期515-519,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11301234;11211171);江西省自然科学基金(20161ACB20006;20142BCB23009;20151BAB201012)资助项目

摘　　要：研究了多维Schrdinger方程的紧致修正交替方向格式.通过对J.Douglas等提出的交替方向格式进行误差分析可以发现其分裂误差远远大于时间离散的截断误差.为提高计算精度和效率,在格式中加入1个扰动项以提高分裂误差的阶数,使时间离散误差占优.数值实验验证了格式的优越性和扰动项的作用.A compact and modified alternative direction implicit （ADI） scheme is contributed to muhidimensional Schrodinger equations. After analyzing the error of Douglas＇ ADI scheme, it is discovered that the splitting error ofthe ADI scheme is much larger than truncation error from time approximation. A perturbation term is inserted into Douglas and Peaceman＇s ADI scheme to improve the accuracy and computational efficiency. Moreover,the order ofsplitting error is bettered and the error from time discretization is dominant. Numerical tests verified the advantages of the new scheme and the important role of perturbation term.

关 键 词：Schrdinger方程 修正交替方向格式 高阶紧致格式. 

分 类 号：O241.8[理学—计算数学]