TY - UNPB
T1 - A randomized Runge-Kutta method for time-irregular delay differential equations
AU - Difonzo, Fabio V.
AU - Przybyłowicz, Paweł
AU - Wu, Yue
AU - Xie, Xinheng
PY - 2024/1/23
Y1 - 2024/1/23
N2 - 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.
AB - 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.
KW - differential equations
KW - delay differential equation
KW - Runge-Kutta
U2 - 10.48550/arXiv.2401.11658
DO - 10.48550/arXiv.2401.11658
M3 - Working Paper/Preprint
BT - A randomized Runge-Kutta method for time-irregular delay differential equations
CY - Ithaca, NY
ER -