随机延迟微分方程平衡方法的均方收敛性与稳定性

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摘要

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.

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关键词：随机延迟微分方程平衡方法均方收敛性稳定性

Abstract：

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

收稿日期: 2009-03-10;

基金资助:

国家自然科学基金资助项目(编号: 10871207).

引用本文:

. 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.

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

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