论文标题
随机runge-kutta方法 - 不精确信息下的稳定性和收敛性
Randomized Runge-Kutta method -- stability and convergence under inexact information
论文作者
论文摘要
我们处理在本地Lipschitz条件下的ODE解决方案的最佳近似，以及有关右侧功能的不精确的离散信息。我们表明，基于标准噪声信息的所有随机算法中，随机两阶段runge-kutta方案是所有随机算法中的最佳方法。我们执行确认我们的理论发现的数值实验。此外，对于最佳算法，我们严格研究了绝对稳定性区域的性质。
We deal with optimal approximation of solutions of ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. We show that the randomized two-stage Runge-Kutta scheme is the optimal method among all randomized algorithms based on standard noisy information. We perform numerical experiments that confirm our theoretical findings. Moreover, for the optimal algorithm we rigorously investigate properties of regions of absolute stability.
