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随机延迟微分方程平衡方法的均方收敛性与稳定性

谭英贤1, 甘四清2, 王小捷2   

  1. 1. 湖南人文科技学院数学系, 湖南娄底 417000;
    2. 中南大学数学科学与计算技术学院, 长沙 410075
  • 收稿日期:2009-03-10 出版日期:2011-02-15 发布日期:2011-03-08
  • 基金资助:

    国家自然科学基金资助项目(编号: 10871207).

谭英贤, 甘四清, 王小捷. 随机延迟微分方程平衡方法的均方收敛性与稳定性[J]. 计算数学, 2011, 33(1): 25-36.

Tan Yingxian, Gan Siqing, Wang Xiaojie. MEAN-SQUARE CONVERGENCE AND STABILITY OF BALANCED METHOD FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2011, 33(1): 25-36.

MEAN-SQUARE CONVERGENCE AND STABILITY OF BALANCED METHOD FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

Tan Yingxian1, Gan Siqing2, Wang Xiaojie2   

  1. 1. Department of Mathematics, Hunan Institute of Humanities Science and technology, Loudi 417000, Hunan, China;
    2. School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China
  • Received:2009-03-10 Online:2011-02-15 Published:2011-03-08

本文讨论求解刚性随机延迟微分方程的平衡方法.证明了随机延迟微分方程平衡方法的均方收敛阶为 1/2.给出了线性随机延迟微分方程平衡方法均方稳定的条件.

This paper investigates the balanced method for solving stiff stochastic delay differential equations. It is proved that the balanced method is mean-square convergent with strong order 1/2. Moreover, we give mean-square stability condition of the balanced method for linear stochastic delay differential equations.

MR(2010)主题分类: 

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