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中立型线性随机延迟微分方程的Euler-Maruyama方法的渐近均方稳定性(英文)

AMS-stability of the Euler-Maruyama method for linear neutral stochastic delay differential equations
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摘要 研究中立型线性随机延迟微分方程的Euler-Maruyama方法的渐近均方稳定性。建立数值方法渐近均方稳定性的定义,给出Euler-Maruyama方法的渐近均方稳定的充分条件,并证明在这些条件下中立型线性随机延迟微分方程的Euler-Maruyama方法是渐近均方稳定的,给出了支持所得结果的数值算例。 Stability of Euler-Maruyama method for linear neutral stochastic delay differential equations is considered. The definition of asymptotic mean square （AMS）-stability of numerical methods is established. The conditions of asymptotic mean square stability of Euler-Maruyama methods for the system are given. It is shown that the Euler-Maruyama method is AMS-stable under these conditions. The numerical examples are presented to support the obtained results.
作者 周立群
机构地区 天津师范大学数学科学学院
出处 《黑龙江大学自然科学学报》 CAS 北大核心 2013年第4期445-452,457,共9页 Journal of Natural Science of Heilongjiang University
基金 Supported by the Natural Science Foundation of China(60974144) the Foundation for Doctors of Tianjin Normal university(52LX34) Development Program in the Science Research Project for Colleges and Universities of Tianjin of China(20100813)
关键词 中立型随机延迟微分方程 渐近均方稳定性 Euler—Maruyama方法 数值解 方差 neutral stochastic delay differential equations asymptotic mean square stability Euler- Maruyama method numerical solution variance
分类号 O241.8 [理学—计算数学]
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黑龙江大学自然科学学报
2013年 第4期

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