On the error of the Euler scheme for approximation of solutions of nonlinear DDEs under inexact information

TL;DR

This paper investigates the Euler method's accuracy for nonlinear delay differential equations when the function evaluations are noisy, providing theoretical error bounds and numerical results.

Contribution

It offers new theoretical bounds on Euler scheme errors for DDEs with noisy evaluations, under nonstandard assumptions.

Findings

Theoretical upper bounds on discretization error are established.

Numerical experiments confirm the theoretical error estimates.

Abstract

We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by informational noise. We provide theoretical upper bounds on the Euler discretization error and present results from the numerical experiments.