Error estimates at low regularity of splitting schemes for NLS
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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 τ^s/2 in L^2 at this level of regularity.
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