A randomized Runge-Kutta method for time-irregular delay differential equations

Difonzo, Fabio V. and Przybyłowicz, Paweł and Wu, Yue and Xie, Xinheng (2024) A randomized Runge-Kutta method for time-irregular delay differential equations. Other. arXiv.org, Ithaca, NY. (https://doi.org/10.48550/arXiv.2401.11658)

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

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