Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations
文献类型：期刊论文
| 作者 | Cui, Jianbo; Hong, Jialin ; Liu, Zhihui
|
| 刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2017-10-05 |
| 卷号 | 263期号:7页码:3687-3713 |
| 关键词 | Stochastic cubic Schrodinger equation Strong convergence rate Central difference scheme Exponential integrability Continuous dependence |
| ISSN号 | 0022-0396 |
| DOI | 10.1016/j.jde.2017.05.002 |
| 英文摘要 | In this paper, we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schrodinger equations driven by a multiplicative Q-Wiener process. Beyond the uniform boundedness of moments for high order derivatives of the exact solution, the key requirement of our approach is the exponential integrability of both the exact and numerical solutions. By constructing and analyzing a Lyapunov functional and its discrete correspondence, we derive the uniform boundedness of moments for high order derivatives of the exact solution and the first order derivative of the numerical solution, which immediately yields the well-posedness of both the continuous and discrete problems. The latter exponential integrability is obtained through a variant of a criterion given by Cox, Hutzenthaler and Jentzen [arXiv:1309.5595]. As a by-product of this exponential integrability, we prove that the exact and numerical solutions depend continuously on the initial data and obtain a large deviation type result on the dependence of the noise with first order strong convergence rate. (C) 2017 Elsevier Inc. All rights reserved. |
| 资助项目 | National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[11290142] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000406354200002 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26294]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Liu, Zhihui |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Cui, Jianbo,Hong, Jialin,Liu, Zhihui. Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2017,263(7):3687-3713. |
| APA | Cui, Jianbo,Hong, Jialin,&Liu, Zhihui.(2017).Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations.JOURNAL OF DIFFERENTIAL EQUATIONS,263(7),3687-3713. |
| MLA | Cui, Jianbo,et al."Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations".JOURNAL OF DIFFERENTIAL EQUATIONS 263.7(2017):3687-3713. |
入库方式： OAI收割
来源：数学与系统科学研究院
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