On the error of the Euler scheme for approximation of solutions of nonlinear DDEs under inexact information
arXiv:2604.0118031.7
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This work addresses numerical stability issues for researchers in computational mathematics, but it is incremental as it extends existing Euler method analysis to noisy conditions.
The paper tackles the problem of approximating solutions to nonlinear delay differential equations using the Euler method when function evaluations are subject to noise, providing theoretical error bounds and numerical results.
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.