NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME
文献类型：期刊论文
| 作者 | Hong, Jialin1 ; Wang, Xu1; Zhang, Liying2
|
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2017 |
| 卷号 | 55期号:1页码:305-327 |
| 关键词 | stochastic Schriidinger equation multiplicative noise unique ergodicity multisymplectic scheme weak error |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/16M1079099 |
| 英文摘要 | We consider a finite dimensional approximation of the stochastic nonlinear Schrodinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the unique ergodicity and the charge conservation law for this finite dimensional approximation are obtained on the unit sphere. To simulate the ergodic limit over long time for the finite dimensional approximation, we discretize it further in the temporal direction to obtain a fully discrete scheme, which inherits not only the stochastic multi-symplecticity and charge conservation law of the original equation but also the unique ergodicity of the finite dimensional approximation. The temporal average of the fully discrete numerical solution is proved to converge to the ergodic limit with order 1 with respect to the time step for a fixed spatial step. Numerical experiments verify our theoretical results on charge conservation, ergodicity, and weak convergence. |
| 资助项目 | National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142] ; National Natural Science Foundation of China[11601514] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000396683300014 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/24832]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Wang, Xu |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.China Univ Min & Technol, Coll Sci, Dept Math, Beijing 100083, Peoples R China |
| 推荐引用方式 GB/T 7714 | Hong, Jialin,Wang, Xu,Zhang, Liying. NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(1):305-327. |
| APA | Hong, Jialin,Wang, Xu,&Zhang, Liying.(2017).NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(1),305-327. |
| MLA | Hong, Jialin,et al."NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.1(2017):305-327. |
入库方式： OAI收割
来源：数学与系统科学研究院
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