Euler scheme for approximation of solution of nonlinear ODEs under inexact information

We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local Holder continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Finally, we present the results of some numerical experiments. (c) 2023 IMACS. Published by Elsevier B.V. All rights reserved.