Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions
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| Format: | Preprint |
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2023
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| _version_ | 1866918444145836032 |
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| author | Ruff, Maximilian Schnaubelt, Roland |
| author_facet | Ruff, Maximilian Schnaubelt, Roland |
| contents | We study time integration schemes for $\dot H^1$-solutions to the energy-(sub)critical semilinear wave equation on $\mathbb{R}^3$. We show first-order convergence in $L^2$ for the Lie splitting and convergence order $3/2$ for a corrected Lie splitting. To our knowledge this includes the first error analysis performed for scaling-critical dispersive problems. Our approach is based on discrete-time Strichartz estimates, including one (with a logarithmic correction) for the case of the forbidden endpoint. Our schemes and the Strichartz estimates contain frequency cut-offs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03245 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions Ruff, Maximilian Schnaubelt, Roland Numerical Analysis Analysis of PDEs 65M15 (Primary) 35B33, 35L71, 65M12 (Secondary) We study time integration schemes for $\dot H^1$-solutions to the energy-(sub)critical semilinear wave equation on $\mathbb{R}^3$. We show first-order convergence in $L^2$ for the Lie splitting and convergence order $3/2$ for a corrected Lie splitting. To our knowledge this includes the first error analysis performed for scaling-critical dispersive problems. Our approach is based on discrete-time Strichartz estimates, including one (with a logarithmic correction) for the case of the forbidden endpoint. Our schemes and the Strichartz estimates contain frequency cut-offs. |
| title | Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions |
| topic | Numerical Analysis Analysis of PDEs 65M15 (Primary) 35B33, 35L71, 65M12 (Secondary) |
| url | https://arxiv.org/abs/2311.03245 |