Euler scheme for approximation of solution of nonlinear ODEs under inexact information
Numerical Analysis
2023-12-13 v2 Numerical Analysis
Abstract
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 H\"older 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.
Keywords
Cite
@article{arxiv.2209.07482,
title = {Euler scheme for approximation of solution of nonlinear ODEs under inexact information},
author = {Natalia Czyżewska and Paweł M. Morkisz and Paweł Przybyłowicz},
journal= {arXiv preprint arXiv:2209.07482},
year = {2023}
}
Comments
18 pages, 9 figures