Error estimates at low regularity of splitting schemes for NLS

Ostermann, Alexander; Rousset, Frédéric; Schratz, Katharina

doi:10.1090/mcom/3676

Error estimates at low regularity of splitting schemes for NLS
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by Alexander Ostermann, Frédéric Rousset and Katharina Schratz HTML | PDF

Math. Comp. 91 (2022), 169-182 Request permission

Abstract:

We study a filtered Lie splitting scheme for the cubic nonlinear Schrödinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows us to handle data in $H^s$ with $0<s<1$ overcoming the standard stability restriction to smooth Sobolev spaces with index $s>1/2$ . More precisely, we prove convergence rates of order $\tau ^{s/2}$ in $L^2$ at this level of regularity.

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