Optimal Error Bounds on the Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Low Regularity Potential and Nonlinearity
DOI10.1137/23m155414xarXiv2302.09262OpenAlexW4390806724MaRDI QIDQ6184514
Publication date: 25 January 2024
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2302.09262
nonlinear Schrödinger equationoptimal error boundexponential wave integratorextended Fourier pseudospectral methodlow regularity nonlinearitylow regularity potential
Smoothness and regularity of solutions to PDEs (35B65) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) 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) Fourier integral operators applied to PDEs (35S30) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- Unnamed Item
- Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation
- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
- A splitting method for the nonlinear Schrödinger equation
- Derivation of the cubic nonlinear Schrödinger equation from quantum dynamics of many-body systems
- Symmetric exponential integrators with an application to the cubic Schrödinger equation
- On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Low regularity exponential-type integrators for semilinear Schrödinger equations
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
- Mathematical theory and numerical methods for Bose-Einstein condensation
- On the splitting method for the nonlinear Schrödinger equation with initial data in \(H^1\)
- Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
- Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity
- A fully discrete low-regularity integrator for the nonlinear Schrödinger equation
- Numerical integrators for continuous disordered nonlinear Schrödinger equation
- Regularized numerical methods for the logarithmic Schrödinger equation
- Effective one particle quantum dynamics of electrons: a numerical study of the Schrödinger-Poisson-X\(_\alpha\) model
- Analysis and Computation for Ground State Solutions of Bose--Fermi Mixtures at Zero Temperature
- Exponential integrators
- Spectral Methods
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
- Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties
- Optimal H1 Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
- Finite difference discretization of the cubic Schrödinger equation
- Spectral Methods and Their Applications
- LOCAL APPROXIMATION FOR THE HARTREE–FOCK EXCHANGE POTENTIAL: A DEFORMATION APPROACH
- Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
- Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schrödinger Equation
- Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
- A General Framework of Low Regularity Integrators
- Error estimates at low regularity of splitting schemes for NLS
- Resonance-based schemes for dispersive equations via decorated trees
- Error estimates of local energy regularization for the logarithmic Schrödinger equation
- A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data
- Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator
- Crank–Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
- Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation
- Regularized Numerical Methods for the Nonlinear Schrödinger Equation with Singular Nonlinearity
