首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  重点论文 |  在线办公 |
 计算数学  2011, Vol. 33 Issue (1): 25-36    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles

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
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
 全文: PDF (418 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料

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.

 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.

 [1] Buckwar E. Introduction to the numerical analysis of stochastic delay differential equations[J]. J. Comput. Appl. Math., 2000, 125: 297-307. [2] Buckwar E. One-step approximatons for stochastic functional differential equations[J]. Appl. Num. Math., 2006, 56: 667-681. [3] Gichman I I , Skorochod A V. Stochastic Differential Equations[M]. Russion: Naukova Dumka, Kiew, 1973. [4] Mao X R. Stochastic Differential Equations and Their Applications[M]. New York: Horwood Publishing, 1997. [5] Alcock J, Burrage K. A note on the balanced method[J]. BIT., 2006, 46: 689-710. [6] Milstein G, Platen E, Schurz H. Balanced implicit methods for stiff stochastic systems[J]. SIAM J. Numer. Anal., 1998, 35: 1010-1019. [7] Saito Y and Mitsui T. Stability analysis of numeric schemes for stochastic differential equations[J]. SIAM J. Numer. Anal., 1996, 33: 2254-2267 [8] Zhang H M, Gan S Q. Mean square convergence of one-step methods for neutral stochastic differential delay equations[J]. Appl. Math. Comput., 2008, 204: 884-890. [9] Liu M Z, Cao W R, Fan Z C. Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation[J]. J. Comput. Appl. Math., 2004, 170: 255-268. [10] Higham D J. An algorithmic introduction to numerical simulation of stochastic differential equations[J]. SIAM Rev., 2001, 43: 525-546. [11] Kahl C, Schurz H. Balanced Milstein Methods for Ordinary SDEs[J]. Monte Carlo Methods and Appl., 2006, 12: 143-170. [12] Mao X R. Razumikhin-type theorems on exponential stability of stochastic functional differential equations[J]. Stochastic process. Appl., 1996, 65: 233-250.
 [1] 吴树林, 王志勇, 黄乘明. Parareal 算法的均方稳定性分析[J]. 计算数学, 2011, 33(2): 113-124. [2] 胡劲松, 胡兵, 徐友才. 耗散对称正则长波方程的有限差分逼近[J]. 计算数学, 2011, 33(2): 177-184. [3] 苏凯, 王锦红, 张宏伟, 王晚生. 显式和对角隐式Rung-Kutta方法求解中立型泛函微分方程的非线性稳定性[J]. 计算数学, 2011, 32(1): 8-22. [4] 王文强, 陈艳萍. 非线性随机延迟微分方程Heun方法的数值稳定性[J]. 计算数学, 2011, 33(1): 69-76. [5] 陈丙振, 游雄. 求解初值问题的 RKNd 方法[J]. 计算数学, 2010, 32(4): 399-412. [6] 张铁, 冯男, 史大涛. 求解椭圆边值问题惩罚形式的间断有限元方法[J]. 计算数学, 2010, 32(3): 275-284. [7] 张在斌, 孙志忠. 一类非线性延迟抛物偏微分方程的Crank-Nicolson型差分格式[J]. 计算数学, 2010, 31(2): 131-140. [8] 胡鹏, 黄乘明. 非线性延迟积分微分方程线性多步法的渐近稳定性[J]. 计算数学, 2010, 31(2): 116-122. [9] 王文强, 陈艳萍. 线性中立型随机延迟微分方程Euler方法的均方稳定性[J]. 计算数学, 2010, 32(2): 206-212. [10] 余越昕. 非线性中立型延迟积分微分方程一般线性方法的稳定性分析[J]. 计算数学, 2010, 32(2): 125-134. [11] 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. [12] 张浩敏, 甘四清, 胡琳. 随机比例方程带线性插值的半隐式Euler方法的均方收敛性[J]. 计算数学, 2009, 31(4): 379-392. [13] 余越昕, 文立平. 非线性中立型延迟积分微分方程线性Θ-方法的渐近稳定性[J]. 计算数学, 2009, 30(4): 241-246. [14] 范振成. 随机延迟微分方程的全隐式Euler方法[J]. 计算数学, 2009, 31(3): 287-298. [15] 刘青霞, 刘发旺. 修正交替方向法求解具有分数阶导数的二维非连续渗流问题[J]. 计算数学, 2009, 31(2): 179-194.
 Copyright 2008 计算数学 版权所有 中国科学院数学与系统科学研究院 《计算数学》编辑部 北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn 本系统由北京玛格泰克科技发展有限公司设计开发 技术支持: 010-62662699 E-mail:support@magtech.com.cn 京ICP备05002806号-10