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

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(Ω)-norm for p∈ [2,+∞). Finally, we report on results of numerical experiments.