线性随机变时滞微分方程指数Euler方法的收敛性和稳定性

doi:10.12286/jssx.j2020-0761

计算数学 ›› 2022, Vol. 44 ›› Issue (3): 339-353.DOI: 10.12286/jssx.j2020-0761

线性随机变时滞微分方程指数Euler方法的收敛性和稳定性

包学忠, 胡琳, 产蔼宁

江西理工大学理学院, 赣州 341000

收稿日期:2020-11-30 出版日期:2022-07-14 发布日期:2022-08-03
基金资助:
国家自然科学基金(11801238,11561028)和江西省教育厅青年资金项目(GJJ170566)资助.

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包学忠, 胡琳, 产蔼宁. 线性随机变时滞微分方程指数Euler方法的收敛性和稳定性[J]. 计算数学, 2022, 44(3): 339-353.

Bao Xuezhong, Hu Lin, Chan Aining. CONVERGENCE AND STABILITY OF EXPONENTIAL EULER METHOD FOR LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH VARIABLE DELAY[J]. Mathematica Numerica Sinica, 2022, 44(3): 339-353.

CONVERGENCE AND STABILITY OF EXPONENTIAL EULER METHOD FOR LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH VARIABLE DELAY

Bao Xuezhong, Hu Lin, Chan Aining

School of science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received:2020-11-30 Online:2022-07-14 Published:2022-08-03

文应用指数Euler方法研究了线性随机变时滞微分方程的收敛性和稳定性;首先,证明了指数Euler方法是$\frac{1}{2}$阶均方收敛的;其次,在解析解均方稳定的前提下,通过跟Euler-Maruyama方法比较发现指数Euler方法在大步长下依然保持解析解的均方稳定性;最后,用数值试验验证了收敛和稳定的结果.

关键词： 随机变时滞微分方程, 指数Euler方法, 均方收敛性, 均方稳定性

In this paper, the convergence and stability of linear stochastic variable delay differential equations are studied by using the exponential Euler method. Firstly, the mean square convergence of the exponential Euler method is proved and the convergence order is 1 2. Secondly, on the premise of the mean square stability of the analytical solution, by comparing with the Euler-Maruyama method, it is found that the exponential Euler method still maintains the mean square stability of the analytical solution in large step size. Finally, the convergence and stability of the results are verified by numerical experiments.

Key words: Stochastic variable delay differential equations, exponential Euler methods, convergence, mean-square stability

MR(2010)主题分类:

65L05
60C20

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摘要

线性随机变时滞微分方程指数Euler方法的收敛性和稳定性

CONVERGENCE AND STABILITY OF EXPONENTIAL EULER METHOD FOR LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH VARIABLE DELAY

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