随机变延迟微分方程平衡方法的收敛性和稳定性  

Convergence and Stability of Balanced Methods for Stochastic Variable Delay Differential Equations

作　　者：包学忠 胡琳[1] 郭慧清 BAO Xuezhong;HU Lin;GUO Huiqing(School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,Jiangxi Province,China)

机构地区：[1]江西理工大学理学院,江西赣州341000

出　　处：《吉林大学学报（理学版）》2020年第6期1345-1356,共12页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11801238,11561028);江西省教育厅青年科学基金(批准号:GJJ170566);江西理工大学创新创业训练计划项目(批准号:DC2018-071)。

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.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.

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 

分 类 号：O241.81[理学—计算数学]