Existence, uniqueness and approximation of solutions to Carathéodory delay differential equations

Abstract

In this paper we address the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with Carathéodory 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.

References in corpus (4)

• A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients
• Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients
• Randomized Runge-Kutta method -- stability and convergence under inexact information
• On mathematical aspects of evolution of dislocation density in metallic materials