随机变延迟微分方程平衡方法的均方收敛性与稳定性  

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

作　　者：包学忠 胡琳[1] Bao Xuezhong;Hu Lin(School of science,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]江西理工大学理学院,赣州341000

出　　处：《计算数学》2021年第3期301-321,共21页Mathematica Numerica Sinica

基　　金：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.

摘　　要：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1/2γ,γ∈(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 1/2γ,γ∈(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 st ability than the explicit-Euler methods.

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：O211.63[理学—概率论与数理统计]