High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates (Q5270351)

scientific article; zbMATH DE number 6734884

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English	High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates	scientific article; zbMATH DE number 6734884

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instance of

scholarly article

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title

High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates (English)

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author

Christophe Besse

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Guillaume Dujardin

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Ingrid Lacroix-Violet

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published in

SIAM Journal on Numerical Analysis

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publication date

23 June 2017

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full work available at URL

https://arxiv.org/abs/1507.00550

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zbMATH Keywords

nonlinear Schrodinger equation

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exponential Runge-Kutta method

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Gross-Pitaevskii equation

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Lawson method

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splitting methods

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MaRDI profile type

MaRDI publication profile

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cites work

Modeling and Computation of Bose-Einstein Condensates: Stationary States, Nucleation, Dynamics, Stochasticity

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Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation

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Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations

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The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics

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On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime

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A Generalized-Laguerre–Fourier–Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose–Einstein Condensates

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A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

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DYNAMICS OF THE GROUND STATE AND CENTRAL VORTEX STATES IN BOSE–EINSTEIN CONDENSATION

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Solitons for the cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

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A Relaxation Scheme for the Nonlinear Schrödinger Equation

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Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation

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An Asymptotic Preserving Scheme Based on a New Formulation for NLS in the Semiclassical Limit

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Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods

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Optimized high-order splitting methods for some classes of parabolic equations

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Splitting methods with complex times for parabolic equations

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Numerical aspects of the nonlinear Schrödinger equation in the semiclassical limit in a supercritical regime

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Stroboscopic averaging for the nonlinear Schrödinger equation

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Symmetric exponential integrators with an application to the cubic Schrödinger equation

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Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations

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One-stage exponential integrators for nonlinear Schrödinger equations over long times

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Finite-difference solutions of a non-linear Schrödinger equation

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The Lie-Trotter splitting for nonlinear evolutionary problems with critical parameters: a compact local error representation and application to nonlinear Schrodinger equations in the semiclassical regime

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Numerical computation of solitons for optical systems

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Exponential Runge-Kutta methods for the Schrödinger equation

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Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential

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The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation

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Resonant time steps and instabilities in the numerical integration of Schrödinger equations.

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Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme

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Splitting integrators for nonlinear Schrödinger equations over long times

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Geometric Numerical Integration

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Solving Ordinary Differential Equations I

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On Krylov Subspace Approximations to the Matrix Exponential Operator

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Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

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Exponential Runge-Kutta methods for parabolic problems.

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Exponential integrators

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Convergence analysis of high-order time-splitting pseudo-spectral methods for rotational Gross-Pitaevskii equations

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A First Course in the Numerical Analysis of Differential Equations

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Fourth-Order Time-Stepping for Stiff PDEs

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Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants

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On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations

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Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation

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Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals

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Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation

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Identifiers

zbMATH Open document ID

1371.35235

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DOI

10.1137/15M1029047

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:5270351