论文标题
关于随机Euler和Runge-Kutta方案的特殊集的属性
On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes
论文作者
论文摘要
我们表明，对于近似ODE的解决方案的广泛的随机算法，特殊集合的概率呈指数衰减，承认某些误差分解。该类包括随机的显式和隐式Euler方案，以及随机的两阶段runge-kutta方案（在不精确的信息下）。我们为IVP的精确解决方案设计一个置信区间，并执行数值实验以说明理论结果。
We show that the probability of the exceptional set decays exponentially for a broad class of randomized algorithms approximating solutions of ODEs, admitting a certain error decomposition. This class includes randomized explicit and implicit Euler schemes, and the randomized two-stage Runge-Kutta scheme (under inexact information). We design a confidence interval for the exact solution of an IVP and perform numerical experiments to illustrate the theoretical results.
