Existence, uniqueness and approximation of solutions to Carath\'eodory delay differential equations

TL;DR

This paper investigates the existence, uniqueness, and approximation of solutions to Carathéodory delay differential equations, introducing a randomized Euler scheme and analyzing its error through numerical experiments.

Contribution

It presents a new randomized Euler scheme for DDEs with Carathéodory functions and provides error analysis and numerical validation.

Findings

Established conditions for existence and uniqueness of solutions.

Developed a randomized Euler approximation method.

Validated the method with numerical experiments.

Abstract

In this paper we address the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with Carath\'eodory type right-hand side functions. We provide construction of randomized Euler scheme for DDEs and investigate its error. We also report results of numerical experiments.