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Superconvergence of Strang splitting for NLS in $T^d$

Philippe Chartier 1, 2, * Florian Méhats 1, 2, * Mechthild Thalhammer 3 Yong Zhang 4
* Corresponding author
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : In this paper we investigate the convergence properties of semi-discretized approximations by Strang splitting method applied to fast-oscillating nonlinear Schr¨odinger equations. In a first step and for further use, we briefly adapt a known convergence result for Strang method in the context of NLS on $T^d$ for a large class of nonlinearities. In a second step, we examine how errors depend on the length of the period $\varepsilon$, the solutions being considered on intervals of fixed length (independent of the period). Our main contribution is to show that Strang splitting with constant step-sizes is unexpectedly more accurate by a factor $\varepsilon$ as compared to established results when the step-size is chosen as an integer fraction of the period, owing to an averaging effect.
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Submitted on : Friday, March 7, 2014 - 11:13:33 AM
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Philippe Chartier, Florian Méhats, Mechthild Thalhammer, Yong Zhang. Superconvergence of Strang splitting for NLS in $T^d$. 2014. ⟨hal-00956714⟩

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