随机延迟微分方程平衡方法的均方收敛性与稳定性

doi:10.12286/jssx.2011.1.25

计算数学 ›› 2011, Vol. 33 ›› Issue (1): 25-36.DOI: 10.12286/jssx.2011.1.25

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. 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).

PDF ( 1262 ) 引用被引次数 ( 31 | 3 )

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. 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.

关键词： 随机延迟微分方程, 平衡方法, 均方收敛性, 稳定性

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.

Key words: stochastic delay differential equations, balanced method, mean-square convergence, stability

MR(2010)主题分类:

60H10
60H35

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摘要

随机延迟微分方程平衡方法的均方收敛性与稳定性

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

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