A mass conserved splitting method for the nonlinear Schr?dinger equation | |
Hua,Dong-Ying1; Li,Xiang-Gui1; Zhu,Jiang2 | |
刊名 | Advances in Difference Equations
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2012-06-21 | |
卷号 | 2012期号:1 |
关键词 | time-splitting finite difference dipolar Bose-Einstein condensates Schr?dinger equation conservation |
ISSN号 | 1687-1847 |
DOI | 10.1186/1687-1847-2012-85 |
英文摘要 | AbstractA mass conserved time-splitting difference method is presented for the one-dimensional dipolar Bose-Einstein condensates (BECs) described by a nonlocal nonlinear Schr?dinger equation with a convolution term. As a result of the singularity in the convolution term, it brings difficulties both in mathematical analysis and in numerical simulations. By properly using the difference scheme to deal with the convolution term, an imaginary time method is given to compute the ground states and then a time-splitting method is obtained for dynamics of dipolar BECs. This time-splitting numerical method is mass conserved everywhere, and it has second-order accuracy and is also unconditionally stable. Numerical results are given to verify the stability and energy conservation when there is no blow up.Mathematics Subject Classification (2010) 65M06; 35Q41. |
语种 | 英语 |
出版者 | Springer International Publishing |
WOS记录号 | BMC:10.1186/1687-1847-2012-85 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/314] ![]() |
专题 | 中国科学院数学与系统科学研究院 |
通讯作者 | Li,Xiang-Gui |
作者单位 | 1.Beijing Information Science and Technology University; School of Applied Science 2.Ministry of Science and Technology; National Laboratory for Scientific Computing |
推荐引用方式 GB/T 7714 | Hua,Dong-Ying,Li,Xiang-Gui,Zhu,Jiang. A mass conserved splitting method for the nonlinear Schr?dinger equation[J]. Advances in Difference Equations,2012,2012(1). |
APA | Hua,Dong-Ying,Li,Xiang-Gui,&Zhu,Jiang.(2012).A mass conserved splitting method for the nonlinear Schr?dinger equation.Advances in Difference Equations,2012(1). |
MLA | Hua,Dong-Ying,et al."A mass conserved splitting method for the nonlinear Schr?dinger equation".Advances in Difference Equations 2012.1(2012). |
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