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

2024/01/22 by Difonzo, Fabio V., Przybyłowicz, Paweł, Wu, Yue +1
#FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.11658

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

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