Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates

Abstract

We investigate a filtered Lie-Trotter splitting scheme for the ``good" Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use of discrete Bourgain spaces, our analysis extends to initial data in $H^s$ for $0<s\le 2$, overcoming the constraint of $s>1/2$ imposed by the bilinear estimate in smooth Sobolev spaces. We establish convergence rates of order ${\tau }^{s/2}$ in $L^2$ for such levels of regularity. Our analytical findings are supported by numerical experiments.

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References in corpus (4)

• Local solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation
• Low regularity full error estimates for the cubic nonlinear Schrödinger equation
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Cited by in corpus (1)

• Error estimates of time-splitting schemes for nonlinear Klein--Gordon equation with rough data