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arXiv · 2506.02778

Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators

Qiumei Huang·Alexander Ostermann·Gangfan Zhong
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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.

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Qiumei Huang, Alexander Ostermann, Gangfan Zhong. 2025-06-03. Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators. https://doi.org/10.1051/m2an%2F2026009

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