Abstract

We consider various filtered time discretizations of the periodic Korteweg–de Vries equation: a filtered exponential integrator, a filtered Lie splitting scheme, as well as a filtered resonance-based discretization, and establish error estimates at low regularity. Our analysis is based on discrete Bourgain spaces and allows us to prove convergence in $L^2$ for rough data $u_0\in H^s$, $s>0$, with an explicit convergence rate.

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