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arXiv · 2311.03245

Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions

Maximilian Ruff·Roland Schnaubelt
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Abstract

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.

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Maximilian Ruff, Roland Schnaubelt. 2023-11-06. Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions. https://doi.org/10.3934/dcds.2025009

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