[1]符芳芳,周媛兰.2维Gross-Pitaevskii方程的辛格式[J].江西师范大学学报(自然科学版),2016,40(06):599-602.
 FU Fangfang,ZHOU Yuanlan.The Symplectic Integrator for Two-Dimensional Gross-Pitaevskii Equations[J].,2016,40(06):599-602.
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2维Gross-Pitaevskii方程的辛格式()
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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:
40
期数:
2016年06期
页码:
599-602
栏目:
出版日期:
2016-12-01

文章信息/Info

Title:
The Symplectic Integrator for Two-Dimensional Gross-Pitaevskii Equations
作者:
符芳芳周媛兰
1.南昌工学院,江西 南昌 330108; 2.江西师范大学数学与信息科学学院,江西 南昌 330022
Author(s):
FU FangfangZHOU Yuanlan
1.Nanchang Institute of Science and Technology,Nanchang Jiangxi 330108,China; 2.College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
辛格式 Gross-Pitaevskii方程 守恒律
Keywords:
symplectic integrator Gross-Pitaevskii equation conservation laws
分类号:
O 241.8
摘要:
提出了2维Gross-Pitaevskii方程的辛格式,该格式能够精确地保持电荷守恒和隐式能量守恒,还分析了该格式的数值误差,最后通过数值例子验证了理论结果.
Abstract:
A symplectic integrator is proposed for the two dimensional Gross-Pitaevskii equations in the letter.It is observed that the proposed scheme keeps the charge exactly unchanged and an implicit energy conservation law.Furthermore,the error of the numerical method is estimated theoretically.The theoretical analysis is illustrated by some numerical examples.

参考文献/References:

[1] Gross E P.Hydrodynamics of a superfluid condensate [J].J Math Phys,1963,4(2):195-207.
[2] Dalfovo F,Giorgini S.Theory of Bose-Einstein condensation in trapped gases [J].Physics,1999,71(3):463-512.
[3] Wang Hanquan.Numerical studies on split-step finite difference method for nonlinear Schr?dinger equations [J].Appl Math Comput,2005,170(1):17-35.
[4] Bao Weizhu.Numerical methods for the nonlinear Schr?dinger equation with nonzero far-field conditions [J].Methods and Applications of Analysis,2004,11(3):1-22.
[5] Kong Linghua,Hong Jialin,Zhang Jingjing.LOD-MS for Gross-Pitaevskii equation in Bose-Einstein condensates [J].Commun Comput Phys,2013,14(1):219-241.
[6] Muruganandam P,Adhikari S K.Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap [J].Comput Phys Commun,2009,180(10):1888-1912.
[7] Feng Kang.On difference schemes and symplectic geometry [C]//Feng Kang.Proceeding of the 1984 Beijing Symposium on Differential Geometry and Differential Equations,Computation of PDEs,Beijing:Science Press,1985:42-58.
[8] Fu Fangfang,Kong Linghua,Wang Lan.Symplectic Euler method for nonlinear high order Schr?dinger equation with a trapped term [J].Adv Appl Math Mech,2009,1(5):699-710.
[9] 符芳芳,孔令华.一类新的含双幂非线性项的Schr?dinger方程的差分格式 [J].江西师范大学学报:自然科学版,2010,34(1):22-26.
[10] Chen Jingbo,Qin Mengzhao,Tang Yifa.Symplectic and multi-symplectic methods for the nonlinear Schr?dinger equations [J].Comput Math with Appl,2002,43(8/9):1095-1106.
[11] 秦孟兆,王雨顺.偏微分方程中的保结构算法 [M].杭州:浙江科学技术出版社,2011.
[12] Wang Yushun,Hong Jialin.Multi-symplectic algorithms for Hamiltonian partial differential equations [J].Commun Appl Math Comput,2013,27(2):163-230.
[13] 黄红,王兰.薛定谔方程的局部1维多辛算法 [J].江西师范大学学报:自然科学版,2011,35(5):455-458.
[14] 徐远,孔令华,王兰,等.带有阻尼项的4阶非线性薛定谔方程的显式辛格式 [J].江西师范大学学报:自然科学版,2013,37(3):244-248.
[15] Wang Zhongcheng,Shao Hezhu.A new kind of discretization scheme for solving a two-dimensional time-independent Schr?dinger equation [J].Comput Phys Commun,2009,180(6):842-849.
[16] Kalogiratou Z,Monovasilis T,Simos T E.Symplectic integrators for the numerical solution of the Schr?dinger equation [J].J Comput Appl Math,2003,158(1):83-92.

备注/Memo

备注/Memo:
收稿日期:2016-05-20基金项目:国家自然科学基金(11301234,11211171)和江西省自然科学基金(20161ACB20006,20151BAB201012,20142BCB23009)资助项目.作者简介:符芳芳(1984-),女,江西南昌人,讲师,主要从事偏微分方程研究.
更新日期/Last Update: 1900-01-01