Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909638475120640 |
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| author | Huang, Qiumei Ostermann, Alexander Zhong, Gangfan |
| author_facet | Huang, Qiumei Ostermann, Alexander Zhong, Gangfan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators Huang, Qiumei Ostermann, Alexander Zhong, Gangfan Numerical Analysis 65M12, 65L06 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. |
| title | Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators |
| topic | Numerical Analysis 65M12, 65L06 |
| url | https://arxiv.org/abs/2506.02778 |