Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme

Abstract

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 Hölder continuous. We provide a detailed error analysis of the Euler algorithm under such nonstandard regularity conditions. Moreover, we report results of numerical experiments.

22 pages, 10 figures

References in corpus (2)

• Modeling and Forecasting of COVID-19 Spreading by Delayed Stochastic Differential Equations
• On mathematical aspects of evolution of dislocation density in metallic materials