Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators
Numerical Analysis
2025-06-06 v1 Numerical Analysis
Abstract
We derive error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in a framework of abstract semilinear evolution equations with operators having non-dense domain. In particular, we investigate nonsmooth data error estimates for the Allen-Cahn and the Burgers' equation. As an application, we apply these nonsmooth data error estimates to split exponential integrators and derive a convergence result in terms of the data.
Cite
@article{arxiv.2506.02778,
title = {Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators},
author = {Qiumei Huang and Alexander Ostermann and Gangfan Zhong},
journal= {arXiv preprint arXiv:2506.02778},
year = {2025}
}