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arXiv · 2312.11071

Low regularity error estimates for high dimensional nonlinear Schr\"odinger equations

Lun Ji·Alexander Ostermann
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Abstract

The filtered Lie splitting scheme is an established method for the numerical integration of the periodic nonlinear Schr\"{o}dinger equation at low regularity. Its temporal convergence was recently analyzed in a framework of discrete Bourgain spaces in one and two space dimensions for initial data in $H^s$ with $0<s\leq 2$. Here, this analysis is extended to dimensions $d=3, 4, 5$ for data satisfying $d/2-1 < s \leq 2$. In this setting, convergence of order $s/2$ in $L^2$ is proven. Numerical examples illustrate these convergence results.

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Lun Ji, Alexander Ostermann. 2023-12-18. Low regularity error estimates for high dimensional nonlinear Schr\"odinger equations. https://doi.org/10.1007/978-3-031-76988-7_13

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