A Randomized Runge-Kutta Method for time-irregular delay differential equations

Abstract

In this paper we investigate the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with the right-hand side functions $f=f(t,x,z)$ that are Lipschitz continuous with respect to $x$ but only Hölder continuous with respect to $(t,z)$. We give a construction of the randomized two-stage Runge-Kutta scheme for DDEs and investigate its upper error bound in the $L^p(\Omega )$-norm for $p\in [2,+\infty )$. Finally, we report on results of numerical experiments.

arXiv admin note: text overlap with arXiv:2204.02016