English

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