| 线性随机分数阶微分方程Euler方法的弱收敛性与弱稳定性 |
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| 引用本文： | 王文强,孙晓莉.线性随机分数阶微分方程Euler方法的弱收敛性与弱稳定性[J].计算数学,2014,36(2):195-204. |
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| 作者姓名： | 王文强 孙晓莉 |
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| 作者单位： | 湘潭大学数学与计算科学学院, 湖南湘潭, 411105 |
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| 基金项目： | 国家自然科学基金（11171352、11271311）. |
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| 摘 要： | 本文主要研究了线性随机分数阶微分方程Euler方法的弱收敛性与弱稳定性.首先构造了数值求解线性随机分数阶微分方程的Euler方法,然后证明该方法是弱稳定的和α阶弱收敛的,文末给出的数值算例验证了所获得的理论结果的正确性.
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| 关 键 词： | 线性随机分数阶微分方程 Euler方法 弱收敛性 弱稳定性 |
| 收稿时间： | 2013-08-02; |
WEAK CONVERGENCE AND WEAK STABILITY OF EULER METHOD FOR LINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION |
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| Wang Wenqiang,Sun Xiaoli.WEAK CONVERGENCE AND WEAK STABILITY OF EULER METHOD FOR LINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION[J].Mathematica Numerica Sinica,2014,36(2):195-204. |
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| Authors: | Wang Wenqiang Sun Xiaoli |
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| Institution: | School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China |
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| Abstract: | The authors mainly study the weak convergence and weak stability of Euler method for linear stochastic fractional differential equation. In this paper, an explicit numerical method for the linear stochastic fractional differential equation is proposed. Weak convergence and weak stability of the Euler method are established. Finally, one numerical example is given. The numerical results demonstrate the effectiveness of the theoretical analysis. |
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| Keywords: | linear stochastic fractional differential equation Euler method weak convergence weak stability |
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