| 随机变延迟微分方程平衡方法的收敛性和稳定性 |
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| 引用本文： | 包学忠,胡琳,郭慧清.随机变延迟微分方程平衡方法的收敛性和稳定性[J].吉林大学学报(理学版),2020,58(6):1345-1356. |
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| 作者姓名： | 包学忠 胡琳 郭慧清 |
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| 作者单位： | 江西理工大学 理学院, 江西 赣州 341000 |
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| 基金项目： | 江西理工大学创新创业训练计划项目;国家自然科学基金;江西省教育厅青年科学基金 |
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| 摘 要： | 利用全隐式数值方法—平衡方法讨论一类随机变延迟微分方程的收敛性和稳定性. 首先, 证明该方程数值解以1/2阶均方收敛到精确解; 其次, 证明该方法能保持解析解的均方稳定性; 最后, 通过数值实验验证理论结果的正确性.
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| 关 键 词： | 随机变延迟微分方程 平衡方法 均方收敛性 均方稳定性 |
Convergence and Stability of Balanced Methods for Stochastic Variable Delay Differential Equations |
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| BAO Xuezhong,HU Lin,GUO Huiqing.Convergence and Stability of Balanced Methods for Stochastic Variable Delay Differential Equations[J].Journal of Jilin University: Sci Ed,2020,58(6):1345-1356. |
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| Authors: | BAO Xuezhong HU Lin GUO Huiqing |
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| Institution: | School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi Province, China |
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| Abstract: | We discussed the convergence and stability by using the fully implicit numerical method—balanced methods for a class of stochastic variable delay differential equations. Firstly, we proved that the numerical solution of the equation converged to the exact solution in 1/2 order mean-square. Secondly, we proved that the method could keep the mean-square stability of the analytical solution. Finally, the correctness of the theoretical results was verified by numerical experiments. |
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| Keywords: | stochastic variable delay differential equation balanced method mean-square convergence mean-square stability |
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