Error estimates at low regularity of splitting schemes for NLS - Archive ouverte HAL
Article Dans Une Revue Mathematics of Computation Année : 2022

Error estimates at low regularity of splitting schemes for NLS

Résumé

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 H^s with 0 > s > 1 0>s>1 overcoming the standard stability restriction to smooth Sobolev spaces with index s > 1 / 2 s>1/2 . More precisely, we prove convergence rates of order τ s / 2 \tau ^{s/2} in L 2 L^2 at this level of regularity.

Dates et versions

hal-03880284 , version 1 (01-12-2022)

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Citer

Alexander Ostermann, Frédéric Rousset, Katharina Schratz. Error estimates at low regularity of splitting schemes for NLS. Mathematics of Computation, 2022, 91 (333), pp.169-182. ⟨10.1090/mcom/3676⟩. ⟨hal-03880284⟩
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