We deal with approximation of solutions of delay differential equations (DDEs) via the classical Euler algorithm. We investigate the pointwise error of the Euler scheme under nonstandard assumptions imposed on the right-hand side function $f$. Namely, we assume that $f$ is globally of at most linear growth, satisfies globally one-side Lipschitz condition but it is only locally H\"older continuous. We provide a detailed error analysis of the Euler algorithm under such nonstandard regularity conditions. Moreover, we report results of numerical experiments.

翻译：我们通过古典Euler算法处理延迟差分方程(DDEs)解决方案的近似问题。我们根据对右侧功能施加的非标准假设调查了Euler 方案在非标准假设下的点误差 $f美元。也就是说,我们假设美元是全球最多线性增长的美元,满足全球单边的Lipschitz条件,但只是局部的H\ older 持续。我们在非标准性条件下对 Euler 算法提供了详细的错误分析。此外,我们报告数字实验的结果。