论文标题
部分可观测时空混沌系统的无模型预测
An adaptive time-stepping fully discrete scheme for stochastic NLS equation: Strong convergence and numerical asymptotics
论文作者
论文摘要
在本文中，我们提出和分析了一个自适应时间步变的完全离散的方案，该方案具有具有乘法噪声的随机非线性schrödinger方程的最佳强收敛顺序。基于分裂技能和自适应策略，获得了数值解决方案的$ H^1 $指数集成性，这是得出强收敛顺序的关键要素。我们表明，拟议的方案与订单$ \ frac12 $在时间和2美元的空间中强烈收敛。为了研究数值渐近行为，我们为数值解决方案建立了较大的偏差原理。这是研究大型偏差原理的第一个结果，用于随机偏微分方程的数值方案，并具有超线性增长的漂移。作为副产品，最终获得了数值和精确解之间的质量误差。
In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schrödinger equation with multiplicative noise. Based on the splitting skill and the adaptive strategy, the $H^1$-exponential integrability of the numerical solution is obtained, which is a key ingredient to derive the strong convergence order. We show that the proposed scheme converges strongly with orders $\frac12$ in time and $2$ in space. To investigate the numerical asymptotic behavior, we establish the large deviation principle for the numerical solution. This is the first result on the study of the large deviation principle for the numerical scheme of stochastic partial differential equations with superlinearly growing drift. And as a byproduct, the error of the masses between the numerical and exact solutions is finally obtained.
