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 计算数学  2011, Vol. 33 Issue (1): 69-76    DOI:
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1. 湘潭大学数学与计算科学学院, 湖南湘潭 411105;
2. 湘潭大学土木工程与力学学院, 湖南湘潭 411105;
3. 华南师范大学数学科学学院, 广州 510631
NUMERICAL STABILITY OF HEUN METHODS FOR NONLINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS
Wang Wenqiang1,2, Chen Yanping3
1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China;
2. Civil Engineering & Machanics College, Xiangtan University, Xiangtan 411105, Hunan, China;
3. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
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Abstract

In this paper, the authors investigated the numerical stability of Heun methods for nonlinear stochastic delay differential equations. When the analytical solution satisfies the conditions of mean-square stability, and if the drift term satisfy some restrictions, then the Heun methods with linear interpolation procedure is exponential mean-square stable and GMS-stable, the Heun methods is mean-square stable(MS-stable). Moreover, these results are also verified by some numerical examples.

 引用本文: . 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. . NUMERICAL STABILITY OF HEUN METHODS FOR NONLINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2011, 33(1): 69-76.

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