Randomized Runge–Kutta method — Stability and convergence under inexact information

We deal with optimal approximation of solutions ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. show that randomized two-stage Runge-Kutta scheme is method among all algorithms based on standard noisy information. perform numerical experiments confirm our theoretical findings. Moreover, for algorithm we rigorously investigate properties regions absolute stability.