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两类半隐式随机Runge-Kutta方法 被引量：3

Two Classes of Semi-implicit Stochastic Runge-Kutta Methods
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摘要 本文针对一般的It随机微分方程,应用彩色树理论构造了两类稳定性较好的强1阶半隐式Runge-Kutta(RK)方法,数值实验证明了所得方法的精度和有效性. In this paper, two classes of semi-implicit Runge-Kutta methods with strong order 1 are presented for the strong solution of Ito stochastic differential equations. These methods have very large stability regions ,and the validity is testified in numerical test.
作者 张诚坚 王志勇
机构地区 华中科技大学数学与统计学院
出处 《应用数学》 CSCD 北大核心 2008年第4期819-825,共7页 Mathematica Applicata
基金 国家自然科学基金(10571066)
关键词 随机微分方程 彩色树 RUNGE-KUTTA 均方稳定 Stochastic differential equations Colored rooted tree Runge-Kutta Meansquare stability
分类号 O241.8 [理学—计算数学]
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参考文献13

  • 1Mao X R. Stochastic Differential Equations and Their Applications[M]. Chichester: Horwood, 1997.
  • 2Kloeden P E, Platen E. Numerical Solution of Stochastic Differential Equations[M]. Berlin:Springer-Verlag,1992.
  • 3Nweton N J. Asymptotically efficient Runge-Kutta methods for a class of Ito and Stratonovich equations [J]. SIAM J. Appl. Math. ,1991,51(2):542-567.
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  • 5Burrage P. Runge-Kutta methods for stochastic differential equations [C]. Australia:University of Queensland, 1999.
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  • 8Komori Y. Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations [J]. J. Comput. Appl. Math. ,2007,203:57-79.
  • 9Butcher J. The Numerical Analysis of Ordinary Differential Equations[M]. New York: Wiley, 1987.
  • 10王志勇.随机泛函微分方程的稳态数值解研究[C].武汉:华中科技大学,2008.

同被引文献29

  • 1Mao X R. Stochastic Differential Equations and Their Applications. Chichester: Horwood Publishing Company, 1997.
  • 2Maruyama G. Continuous Markov processes and stochastic equations. Rendiconti del Circolo Matematico di PalermoRend. 1955, 4(1): 48-90.
  • 3Milstein G N. Approximate integration of stochastic differential equations. Theory of Proba- bility and its Applications. 1974, 19(3): 557-562.
  • 4Burrage K and Burrage P M. High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Applied Numerical Mathematics. 1996, 22(1): 81-101.
  • 5Tian T H and Burrage K. Two-stage stochastic Runge-Kutta methods for stochastic differential equations. BIT. 2002, 42(3): 625-643.
  • 6Wang P. Three-stage stochastic Runge-Kutta methods for stochastic differential equations. Journal of Computational and Applied Mathematics. 2008, 222(2): 324-332.
  • 7Butcher J C. Numerical Methods for Ordinary Differential Equations. Chichester: John Wiley and Sons, 2003.
  • 8Komori Y, Mitsui T, Sugiura H. Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations. BIT Numerical Mathematics. 1997, 37(1): 43-66.
  • 9Burrage P M. Runge-Kutta methods for stochastic differential equations. University of Queens-land, 1999.
  • 10Burrage t(, Burrage P M. Order conditions of stochastic Runge Kutta methods by B-series. SIAM Journal Numerical Analysis. 2000, 38(5): 1626-1646.

引证文献3

应用数学
2008年 第4期

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