Error estimates at low regularity of splitting schemes for NLS

DOI10.1090/mcom/3676zbMath1482.65197arXiv2012.14146OpenAlexW3174006813MaRDI QIDQ5018369

Katharina Schratz, Frédéric Rousset, Alexander Ostermann

Publication date: 16 December 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.14146

zbMATH Keywords

nonlinear Schrödinger equationFourier pseudospectral method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items

An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation, Optimal Error Bounds on the Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Low Regularity Potential and Nonlinearity

Cites Work

• Unnamed Item
• Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation
• A splitting method for the nonlinear Schrödinger equation
• Geometric numerical integration and Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• Solving Ordinary Differential Equations I
• Numerical Dispersive Schemes for the Nonlinear Schrödinger Equation
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
• Classical and Multilinear Harmonic Analysis
• A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data