期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

两种半隐式三阶随机Runge-Kutta方法 被引量：2

Two classes of three-stage semi-implicit stochastic Runge-Kutta methods
下载PDF
导出
摘要 根据彩色树理论,构造了两种求解Stratonovich型随机微分方程的半隐式三阶随机Runge-Kutta方法,给出了这两种方法的稳定性分析,其稳定区域比现有方法的稳定区域大;数值模拟的结果表明两个方法都具有较高的精度。 According to colored rooted tree theory, this paper presents two classes of three-stage semi-implicit stochastic Runge-Kutta methods for solving Stratonovich type stochastic differential equations, and analyzes their mean square stability. The stable regions of these methods are larger than those of the extant methods. The numerical simulation results show the high accuracy of the methods in this paper.
作者 朱晓临 王子洁 李井刚
机构地区 合肥工业大学数学学院计算科学与模拟仿真研究所
出处 《计算机工程与应用》 CSCD 2012年第15期49-53,128,共6页 Computer Engineering and Applications
基金 教育部科学技术研究重大项目(No.309017) 安徽省自然科学基金(No.11040606M06) 教育部第38批留学回国人员科研启动基金
关键词 随机微分方程 彩色树 三阶随机Runge-Kutta方法 均方稳定 stochastic differential equations colored rooted tree three-stage stochastic Runge-Kutta method mean square stability
分类号 O241.8 [理学—计算数学]
  • 相关文献

参考文献11

  • 1Kloeden P E, Platen E.Numerical solution of stochastic differential equations[M].Berlin: Springer-Verlag, 1995: 161-221.
  • 2Tian T H, Burrage K.Implicit Taylor methods for stiff stochastic differential equations[J].Appl Numer Math,2001, 38: 167-185.
  • 3Saito Y, Mitsui T.Stability analysis of numerical schemes for stochastic differential equations[J].SIAM J Numer Anal, 1996,33 (6) : 2254-2267.
  • 4Higham D J.Mean-square and asymptotic stability of the stochastic theta method[J].SIAM J Numer Anal,2000,38 (3) :753-769.
  • 5Burrage P M.Runge-Kutta methods for stochastic differential equations[D].Brisbane, Australia: the University of Queensland, 1999.
  • 6Burrage K,Burrage P M.High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations[J].Appl Numer Math, 1996,22 : 81-101.
  • 7Tian T H,Burrage K.Two-stage stochastic Runge-Kutta methods for stochastic differential equations[J].BIT, 2002, 42 (3) : 625 -643.
  • 8Komori Y.Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations[J].J Comput Appl Math, 2007,203 : 57-79.
  • 9Burrage K, Burrage P K.Order condition of stochastic Runge-Kutta methods by B-series[J].SIAM J Numer Anal, 2000,38: 1626-1646.
  • 10王鹏,吕显瑞,张伸煦.求解随机微分方程的三级半隐式随机龙格库塔方法[J].吉林大学学报（理学版）,2008,46(2):219-223. 被引量：10

二级参考文献7

  • 1Milstein G N. Approximate Integration of Stochastic Differential Equations [J]. Theor Prob Appl, 1974, 19: 557-562.
  • 2Rumelin W. Numerical Treatment of Stochastic Differential Equations [ J]. SIAM J Numer Anal, 1982, 19(3): 604-613.
  • 3Tian T H, Burrage K. Two-stage Stochastic Runge-Kutta Methods for Stochastic Differential Equations [ J ]. BIT, 2002, 42(3) : 625-643.
  • 4Burrage K, Burrage P M. High Strong Order Explicit Runge-Kutta Methods for Stochastic Ordinary Differential Equations [J]. Appl Numer Math, 1996, 22: 81-101.
  • 5Milstein G N. Numerical Integration of Stochastic Differential Equations [ M ]. Dordrecht : Kluwer Academic Publishers, 1995.
  • 6Burrage P M. Runge-Kutta Methods for Stochastic Differential Equations [ D] : [ Ph D Thesis]. Brisbane, Australia: University of Queensland, 1999.
  • 7Kloeden P E, Platen E. Numerical Solution of Stochastic Differential Equations [ M ]. Berlin : Springer-Verlag, 1992.

共引文献9

同被引文献15

  • 1Lu Qiming.Schneider M K.PitchfordJ W. Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth[J]. Theoretical Population Biology. 2008. 74(1): 74-83.
  • 2蒲兴成,张毅.随机微分方程及其在数理金融中的应用[M].北京:科学出版社,2010:111-156.
  • 3Kloeden P EvPlaten E. Numerical solution of stochastic dif?ferential equations[MJ. Berlin: Springer-Verlag. 1995: 75-22I.
  • 4Tian T HvBurrage K. Implicit Taylor methods for stiff sto?chastic differential equations[J]. Applied Numerical Math?ematics. 2001. 38(1): 167-185.
  • 5Burrage K. ? Burrage P M High strong order explicit Runge?Kutta methods for stochastic ordinary differential equations[J]. Applied Numerical Mathematics. 1996.22(l) : 81-lOI.
  • 6Burrage K. Burrage P M Order conditions of stochastic Runge-Kutta methods by B-series[J]. SIAMJournal on Numerical Analysis.Eoul , 38(5) : 1626-1646.
  • 7Tian T H. Burrage K. Two-stage stochastic Runge-Kutta methods for stochastic differential equations[J]. BIT. 2002.42(3) :625-643.
  • 8Soheili A Rs Namjoo M Strong approximation of stochastic differential equations with Runge-Kutta methods[J]. WorldJournal of Modeling and Simulation. 2008. 4 (2) :83-93.
  • 9Bastani A F. Hosseini S M. On mean-square stability prop?erties of a new adaptive stochastic Runge-Kutta method[J].Journal of Computational and Applied Mathematics. 2009.224: 556- 564.
  • 10Costabile F. Napoli A Economical Runge-Kutta methods with strong global order one for stochastic differential e?quations[J]. Applied Numerical Mathematics. 2011. 201: 160-169.

引证文献2

计算机工程与应用
2012年 第15期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部