[1]曾文平.Schrdinger方程一族高精度恒稳差分格式[J].华侨大学学报(自然科学版),2004,25(3):237-240.[doi:10.3969/j.issn.1000-5013.2004.03.003]
　Zeng Wenping.A Family of Absolutely Stable Difference Schemes of High Accuracy for Solving Schrdinger Equation[J].Journal of Huaqiao University(Natural Science),2004,25(3):237-240.[doi:10.3969/j.issn.1000-5013.2004.03.003]
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Schrdinger方程一族高精度恒稳差分格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第25卷
期数:
2004年第3期
页码:
237-240
栏目:
出版日期:
2004-07-20

文章信息/Info

Title:
A Family of Absolutely Stable Difference Schemes of High Accuracy for Solving Schrdinger Equation
文章编号:
1000-5013(2004)03-0237-04
作者:
曾文平
华侨大学数学系 福建泉州362021
Author(s):
Zeng Wenping
Dept. of Math., Huaqiao Univ., 362021, Quanzhou, China
关键词:
Schrdinger方程;  差分格式;  高精度;  绝对隐定
Keywords:
Schrdinger equation;  difference scheme;  high accuracy;  absolutely stable
分类号:
O411.1
DOI:
10.3969/j.issn.1000-5013.2004.03.003
文献标志码:
A
摘要:
Schrodinger方程 u t=i 2 u x2,可构造一族含双参数的三层高精度隐式差分格式 当参数α =1/ 2,β =0时得到一个双层格式 证明该格式对任意非负参数α≥ 0,β≥ 0都是绝对稳定的,并且其截断误差阶为O(Δt2 +Δx4) 数值例子表明,文中所建立的差分格式是有效的,理论分析与实际计算相吻合
Abstract:
For solving Schrdinger equation u t =i 2 ux2, it is feasible to construct a family of three layer, high accurate and implicit difference schemes containing two parameters. A three layer difference scheme is obtained in case α =12 and β =0; and this difference scheme is proved to be absolutely stable for arbitrarily chosen non negative parameter, with its truncation error in the order of O( Δ t 2+Δ x 4). The difference scheme constructing here is proved by numerical example to be effective, and its theoretical analysis tallies with practical computation.

参考文献/References:

[1] Chan T F, Lee D, Shen L J. Stable explicit scheme for equation of the Schrdinger type [J]. SIAM Journal on Numerical Analysis, 1986(2):274-281.doi:10.1137/0723019.
[2] 林鹏程. Schrdinger型方程的三层显式格式 [J]. 计算数学, 1988(3):328-331.
[3] MILLER J J H. On the location of zeros of certain classes of polynonials with applications to numerical analysis [J]. Journal of the Institute of Mathematics and Its Applications, 1971(8):397-406.doi:10.1093/imamat/8.3.397.

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更新日期/Last Update: 2014-03-23