Razumikhin-type technique on stability of exact and numerical solutions for the nonlinear stochastic pantograph differential equations
Razumikhin-type technique on stability of exact and numerical solutions for the nonlinear stochastic pantograph differential equations
复制标题
DOI：
10.1007/s10543-018-0723-z
复制
发表时间：
2018-09
影响因子：
1.5
通讯作者：
Ping Guo;Chong-Jun Li
中科院分区：
文献类型：
--
作者：
Ping Guo;Chong-Jun Li
本文建立了随机比例微分方程解的矩多项式稳定性的Razumikhin型定理，改进了现有的随机Razumikhin型定理。利用离散Razumikhin型技巧，构造了随机比例微分方程解的一般数值格式的稳定性条件。稳定性主要包括全局矩渐近稳定性和矩多项式稳定性。利用构造的数值解稳定的条件，我们讨论了两种特殊的数值方法，即Euler-Maruyama方法和反向Euler-Maruyama方法的稳定性。最后给出了一个算例，说明了矩多项式稳定性与理论结果的一致性。
In this paper, we establish Razumikhin-type theorems onth moment polynomial stability of exact solution for the stochastic pantograph differential equations, which improves the existing stochastic Razumikhin-type theorems. By using discrete Razumikhin-type technique, we construct conditions for the stability of general numerical scheme of the stochastic pantograph differential equations (SPDEs). The stabilities mainly conclude the globalth moment asymptotically stability andth moment polynomial stability. Using the conditions constructed for the stability of the numerical solutions, we discuss the stability of two special numerical methods, namely the Euler–Maruyama method and the backward Euler–Maruyama method. Finally, an example is given to illustrate the consistence with the theoretical results onth moment polynomial stability.