On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes
Numerical Analysis
2022-02-04 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2202.01683,
title = {On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes},
author = {Tomasz Bochacik},
journal= {arXiv preprint arXiv:2202.01683},
year = {2022}
}