Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation

DOI10.1016/j.jmaa.2016.05.014zbMath1339.65152OpenAlexW2387639988MaRDI QIDQ294130

Johannes Eilinghoff, Katharina Schratz, Roland Schnaubelt

Publication date: 9 June 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.05.014

zbMATH Keywords

interpolationstabilityerror analysisnonlinear Schrödinger equationsplittingfractional convergence order

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Low regularity exponential-type integrators for semilinear Schrödinger equations ⋮ Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces ⋮ Exponential collocation methods based on continuous finite element approximations for efficiently solving the cubic Schrödinger equation ⋮ Optimal Error Bounds on the Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Low Regularity Potential and Nonlinearity ⋮ Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation ⋮ A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation ⋮ Strang splitting for a semilinear Schrödinger equation with damping and forcing ⋮ On the splitting method for the nonlinear Schrödinger equation with initial data in \(H^1\) ⋮ Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations ⋮ Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity ⋮ A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data ⋮ Error estimates at low regularity of splitting schemes for NLS ⋮ Optimal convergence and long-time conservation of exponential integration for Schrödinger equations in a normal or highly oscillatory regime

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