A Randomized Runge-Kutta Method for time-irregular delay differential equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914647224877056 |
|---|---|
| author | Difonzo, Fabio V. Przybyłowicz, Paweł Wu, Yue Xie, Xinheng |
| author_facet | Difonzo, Fabio V. Przybyłowicz, Paweł Wu, Yue Xie, Xinheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11658 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Randomized Runge-Kutta Method for time-irregular delay differential equations Difonzo, Fabio V. Przybyłowicz, Paweł Wu, Yue Xie, Xinheng Numerical Analysis Probability 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. |
| title | A Randomized Runge-Kutta Method for time-irregular delay differential equations |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2401.11658 |