| 线性随机延迟积分微分方程Euler-Maruyama方法的稳定性 |
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| 引用本文： | 胡鹏,黄乘明. 线性随机延迟积分微分方程Euler-Maruyama方法的稳定性[J]. 计算数学, 2010, 32(1): 105-112 |
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| 作者姓名： | 胡鹏 黄乘明 |
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| 作者单位： | 华中科技大学数学与统计学院,武汉,430074 |
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| 基金项目： | 中国国家自然科学基金 |
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| 摘 要： | 本文研究一类线性随机延迟积分微分方程Euler-Maruyama方法的MS-稳定性.首先,我们讨论方程真解的均方指数稳定性条件.然后,在此假设条件下,证明了带有复合梯形公式的Euler-Maruyama方法是MS-稳定的.最后,数值试验验证了本文的结论.
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| 关 键 词： | 线性随机延迟积分微分方程 MS-稳定性 Euler-Maruyama方法 复合梯形公式 |
| 收稿时间： | 2009-03-25 |
STABILITY OF EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS |
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| Hu Peng,Huang Chengming. STABILITY OF EULER-MARUYAMA METHOD FOR LINEAR STOCHASTIC DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2010, 32(1): 105-112 |
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| Authors: | Hu Peng Huang Chengming |
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| Affiliation: | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | This paper is concerned with the MS-stability of Euler-Maruyama method for a class of linear stochastic delay integro-differential equations. First, we discuss the sufficient conditions of mean-square exponential stability for the true solution of these equations. And then, under such conditions, it is shown that the Euler-Maruyama method with composite trapezoidal rule is MS-stable. At last, we validate our conclusions by numerical experiments. |
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| Keywords: | linear stochastic delay integro-differential equations MS-stability Euler-Maruyama method composite trapezoidal rule |
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