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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2023

A symmetric low-regularity integrator for the nonlinear Schrödinger equation

Intégrateur symétrique à basse régularité pour l'équation de Schrödinger non-linéaire

Résumé

We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schrödinger (NLS) equation beyond classical Fourier-based techniques. We show fractional convergence of the scheme in L 2-norm, from first up to second order, both on the torus T d and on a smooth bounded domain Ω ⊂ R d , d ≤ 3, equipped with homogeneous Dirichlet boundary condition. The new scheme allows for a symmetric approximation to the NLS equation in a more general setting than classical splitting, exponential integrators, and low-regularity schemes (i.e. under lower regularity assumptions, on more general domains, and with fractional rates). We motivate and illustrate our findings through numerical experiments, where we witness better structure preserving properties and an improved error-constant in low-regularity regimes.
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Dates et versions

hal-04212978 , version 1 (20-09-2023)
hal-04212978 , version 2 (12-02-2024)

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Yvonne Alama Bronsard. A symmetric low-regularity integrator for the nonlinear Schrödinger equation. IMA Journal of Numerical Analysis, 2023, ⟨10.1093/imanum/drad093⟩. ⟨hal-04212978v2⟩
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