On time-splitting methods for nonlinear Schrödinger equation with highly oscillatory potential
From MaRDI portal
Publication:3304878
DOI10.1051/m2an/2020006zbMath1451.65163OpenAlexW2943364494MaRDI QIDQ3304878
Publication date: 3 August 2020
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1051/m2an/2020006
error estimatesnonlinear Schrödinger equationStrang splittingLie-Trotter splittinguniformly accuratehighly oscillatory potential
Stability and convergence of numerical methods for ordinary differential equations (65L20) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for initial value problems involving ordinary differential equations (65L05) 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) Error bounds for numerical methods for ordinary differential equations (65L70)
Related Items
A uniformly first-order accurate method for Klein-Gordon-Zakharov system in simultaneous high-plasma-frequency and subsonic limit regime ⋮ Uniformly accurate nested Picard iterative schemes for nonlinear Schrödinger equation with highly oscillatory potential ⋮ Numerical methods for some nonlinear Schrödinger equations in soliton management ⋮ Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations ⋮ Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity
Cites Work
- Unnamed Item
- Unnamed Item
- Nonlinear Schrödinger equation with time dependent potential
- On growth of Sobolev norms in linear Schrödinger equations with time dependent Gevrey potential
- The energy-critical defocusing NLS on \({\mathbb{T}}^{3}\)
- On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit. II. Analytic regularity
- Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
- Geometric numerical integration and Schrödinger equations
- Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime
- Solving highly-oscillatory NLS with SAM: numerical efficiency and long-time behavior
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- Exponential sums and nonlinear Schrödinger equations
- A uniformly accurate multiscale time integrator spectral method for the Klein-Gordon-Zakharov system in the high-plasma-frequency limit regime
- Uniformly accurate particle-in-cell method for the long time solution of the two-dimensional Vlasov-Poisson equation with uniform strong magnetic field
- Growth of Sobolev norms in linear Schrödinger equations with quasi-periodic potential
- Error analysis of the Strang time-splitting Laguerre-Hermite/Hermite collocation methods for the Gross-Pitaevskii equation
- A uniformly and optimally accurate multiscale time integrator method for the Klein-Gordon-Zakharov system in the subsonic limit regime
- A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations
- Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials
- Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
- Long time dynamics of Schrödinger and wave equations on flat tori
- On error estimates of an exponential wave integrator sine pseudospectral method for the Klein-Gordon-Zakharov system
- Convergence of a split-step Hermite method for the Gross-Pitaevskii equation
- Spectral Methods
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- FROM THE KLEIN–GORDON–ZAKHAROV SYSTEM TO THE NONLINEAR SCHRÖDINGER EQUATION
- Logarithmic Bounds on Sobolev Norms for Time Dependent Linear Schrödinger Equations
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
- Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations
- Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to the classical NLS splitting
- A Uniformly and Optimally Accurate Method for the Zakharov System in the Subsonic Limit Regime
- Uniformly Accurate Oscillatory Integrators for the Klein--Gordon--Zakharov System from Low- to High-Plasma Frequency Regimes
- Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime
- Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations
- A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime
- Symmetric high order Gautschi-type exponential wave integrators pseudospectral method for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
- Geometric Numerical Integration
- Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations
- Multiscale particle-in-cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson equation with strong magnetic field
