Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators
Abstract
We derive rigorous error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in the framework of abstract semi-linear evolution equations, allowing for operators with non-dense domains. The results provide a foundation for establishing error estimates for nonsmooth data in prototypical problems such as the Allen-Cahn and Burgers equations. Furthermore, we apply these estimates to the analysis of split exponential integrators, yielding convergence results expressed explicitly in terms of the prescribed data.
Fields of Study & Subjects
Numerical methods for differential equations
Advanced Numerical Methods in Computational Mathematics
Model Reduction and Neural Networks
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Volume
- 60
- Issue
- 2
- Pages
- 495–515
- Publication date
- 27 January 2026
- Language
- EN