Year: 2024
Type: preprint
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 $p\in [2,+\infty)$. Finally, we report on results of numerical experiments.
Source: arXiv (Cornell University)
Institution: AGH University of Krakow
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391158535