DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY
文献类型：期刊论文
| 作者 | Hong, Jialin ; Zhai, Shuxing; Zhang, Jingjing
|
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2011 |
| 卷号 | 49期号:5页码:2017-2038 |
| 关键词 | stochastic differential equation in the Stratonovich sense conserved quantity discrete gradient splitting technique mean-square convergence |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/090771880 |
| 英文摘要 | General autonomous stochastic differential equations (SDEs) driven by one-dimensional Brownian motion in the Stratonovich sense with a conserved quantity I(y) are considered. Relying on this conserved quantity, an equivalent "skew gradient" (SG) form of original SDEs is constructed. With the aim of constructing conserved numerical methods, direct discrete gradient approaches which approximate directly the SG system lead to two conserved methods. In indirect discrete gradient approaches, we first split the SG system into subsystems which preserve the original conserved quantity, then apply direct discrete gradient approaches to subsystems to produce two composition schemes. The mean-square convergence of order 1 for these four methods depends on the assumptions that the coefficients of SDEs are Lipschitz continuous with bounded second moments along the solution of SDEs, are twice continuous differentiable, and have derivatives that are uniformly bounded. Three numerical experiments are presented to verify our theoretical analysis and show the advantages of these methods. |
| 资助项目 | Director Innovation Foundation of ICMSEC ; AMSS ; Foundation of CAS ; NNSFC[60771054] ; Special Funds for Major State Basic Research Projects of China[2005CB321701] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000296605600013 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/12051]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Hong, Jialin |
| 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 | Hong, Jialin,Zhai, Shuxing,Zhang, Jingjing. DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2011,49(5):2017-2038. |
| APA | Hong, Jialin,Zhai, Shuxing,&Zhang, Jingjing.(2011).DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY.SIAM JOURNAL ON NUMERICAL ANALYSIS,49(5),2017-2038. |
| MLA | Hong, Jialin,et al."DISCRETE GRADIENT APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY".SIAM JOURNAL ON NUMERICAL ANALYSIS 49.5(2011):2017-2038. |
入库方式： OAI收割
来源：数学与系统科学研究院
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