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随机变延迟微分方程平衡方法的均方收敛性与稳定性

包学忠, 胡琳   

  1. 江西理工大学理学院, 赣州 341000
  • 收稿日期:2019-07-31 出版日期:2021-08-15 发布日期:2021-08-20
  • 基金资助:
    国家自然科学基金(11801238,11561028),江西省教育厅青年资金项目(GJJ170566),江西理工大学创新创业训练计划项目(DC2018-071)资助.

包学忠, 胡琳. 随机变延迟微分方程平衡方法的均方收敛性与稳定性[J]. 计算数学, 2021, 43(3): 301-321.

Bao Xuezhong, Hu Lin. MEAN SQUARE CONVERGENCE AND STABILITY OF BALANCED METHODS FOR STOCHASTIC VARIABLE DELAY DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2021, 43(3): 301-321.

MEAN SQUARE CONVERGENCE AND STABILITY OF BALANCED METHODS FOR STOCHASTIC VARIABLE DELAY DIFFERENTIAL EQUATIONS

Bao Xuezhong, Hu Lin   

  1. School of science, Jiangxi University of Science and Technology, Ganzhou 341000, China
  • Received:2019-07-31 Online:2021-08-15 Published:2021-08-20
针对一类变延迟微分方程,应用全隐式方法—平衡方法,研究了其收敛性和稳定性.结果表明平衡方法以$\frac{1}{2}\gamma,\gamma\in(0,1]$阶收敛到精确解;并且强平衡方法和弱平衡方法都能保持解析解的均方稳定性;进一步数值实验验证了算法理论分析的正确性,并且表明全隐式的平衡方法比显式方法—Euler方法具有更好的稳定性.
The convergence and stability of a class of variable delay differential equations are studied by using a fully implicit method balanced methods. The results show that the balanced methods converges to the exact solution of order $\frac{1}{2}\gamma, \gamma\in(0, 1]$; Moreover, both the strong balanced methods and the weak balanced methods can reproduce the mean-square stability of the system with sufficiently small stepsize $h$; Further, some numerical experiments included in the paper illustrate the theoretical results, and show that the fully implicit balanced methods has better stability than the explicit—Euler methods.

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