| 一类随机微分方程Runge-Kutta方法的指数稳定性 |
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| 引用本文： | 庞立君,朱永忠. 一类随机微分方程Runge-Kutta方法的指数稳定性[J]. 河海大学学报(自然科学版), 2008, 36(3): 33-432. DOI: 10.3876/j.issn.1000-1980.2008.03.032 |
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| 作者姓名： | 庞立君 朱永忠 |
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| 作者单位： | 河海大学理学院,江苏,南京,210098;河海大学理学院,江苏,南京,210098 |
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| 摘 要： | 为进一步研究随机微分方程的稳定性,给出了随机微分方程的二级Runge-Kutta方法的算法格式,研究了二级显式随机Runge-Kutta方法的均方稳定和指数稳定的条件,并证明了对于线性检验方程,均方稳定性和指数稳定性的关系.
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| 关 键 词： | 随机微分方程 Runge-Kutta方法 均方稳定性 指数稳定性 线性检验方程. |
| 文章编号： | 1000-1980(2008)03-0430-03 |
| 修稿时间： | 2007-07-16 |
Exponential stability of Runge-Kutta methods for a class of stochastic differential equations |
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| PANG Li-jun,ZHU Yong-zhong. Exponential stability of Runge-Kutta methods for a class of stochastic differential equations[J]. Journal of Hohai University (Natural Sciences ), 2008, 36(3): 33-432. DOI: 10.3876/j.issn.1000-1980.2008.03.032 |
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| Authors: | PANG Li-jun ZHU Yong-zhong |
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| Abstract: | In order to research the stability of stochastic differential equations,the two-step Runge-Kutta methods for solving these equations are presented, and the mean square stability and exponential stability conditions of the methods are discussed.The relationship between the mean square stability and exponential stability for linear test equations is also provided. |
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| Keywords: | stochastic differential equation Runge-Kutta methods mean square stability exponential stability linear test equation |
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