On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross–Pitaevskii equations
From MaRDI portal
Publication:5026521
DOI10.1080/00207160.2018.1437911zbMath1499.35522OpenAlexW2790724874MaRDI QIDQ5026521
Qinglin Tang, Jiwei Zhang, Xavier Antoine
Publication date: 8 February 2022
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160.2018.1437911
conservation propertiesfractional Schrödinger equationdiscretization schemesfast implementationaccuracy orderdynamical lawsfractional Gross-Pitaevskii equations
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional ordinary differential equations (34A08) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items (20)
High order WSGL difference operators combined with Sinc-Galerkin method for time fractional Schrödinger equation ⋮ Lie-Trotter operator splitting spectral method for linear semiclassical fractional Schrödinger equation ⋮ Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation ⋮ Smoothing effect and exponential stability of discrete-time Schrödinger equation with fractional regularization term ⋮ Bounded solutions of second order of accuracy difference schemes for semilinear fractional Schrödinger equations ⋮ A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation ⋮ Accurate Absorbing Boundary Conditions for the Two-Dimensional Nonlocal Schrödinger Equations ⋮ A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation ⋮ Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions ⋮ Nonextensive Gross Pitaevskii Equation ⋮ BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation ⋮ Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation ⋮ Efficient Numerical Computation of Time-Fractional Nonlinear Schrödinger Equations in Unbounded Domain ⋮ An efficient Fourier spectral exponential time differencing method for the space-fractional nonlinear Schrödinger equations ⋮ Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation ⋮ Improved error bounds of the Strang splitting method for the highly oscillatory fractional nonlinear Schrödinger equation ⋮ Fast Evaluation of Artificial Boundary Conditions for Advection Diffusion Equations ⋮ Two energy-preserving numerical models for a multi-fractional extension of the Klein-Gordon-Zakharov system ⋮ A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations ⋮ Error analysis and numerical simulations of Strang splitting method for space fractional nonlinear Schrödinger equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- A new difference scheme for the time fractional diffusion equation
- Solving the time-fractional Schrödinger equation by Krylov projection methods
- A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
- Approximate solutions to time-fractional Schrödinger equation via homotopy analysis method
- A stable numerical method for multidimensional time fractional Schrödinger equations
- A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars
- Mittag-Leffler functions and their applications
- Fractional Heisenberg equation
- Numerical analysis and physical simulations for the time fractional radial diffusion equation
- Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations
- Space-time fractional Schrödinger equation with time-independent potentials
- Numerical simulations of 2D fractional subdiffusion problems
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Fractional quantum mechanics and Lévy path integrals
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations
- On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions
- The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations
- Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods
- The accuracy and stability of an implicit solution method for the fractional diffusion equation
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Fractional Schrödinger dynamics and decoherence
- Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
- Time fractional Schrödinger equation revisited
- Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
- A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations
- Finite difference/spectral approximations for the time-fractional diffusion equation
- A perfectly matched layer approach to the nonlinear Schrödinger wave equations
- A fully discrete difference scheme for a diffusion-wave system
- The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrödinger equation arising in quantum mechanics
- Fractals and quantum mechanics
- An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
- Modeling and Computation of Bose-Einstein Condensates: Stationary States, Nucleation, Dynamics, Stochasticity
- An implicit finite-difference time-stepping method for a sub-diffusion equation, with spatial discretization by finite elements
- Spectral Methods
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- Numerical Simulation of the Nonlinear Schrödinger Equation with Multidimensional Periodic Potentials
- High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations
- Mean field dynamics of boson stars
- Generalized fractional Schrödinger equation with space-time fractional derivatives
- Fractional Schrodinger wave equation and fractional uncertainty principle
- Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
- Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation
- Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
- Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
- A Relaxation Scheme for the Nonlinear Schrödinger Equation
- Fast Convolution for Nonreflecting Boundary Conditions
- Time fractional Schrödinger equation
- Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations
- Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
- Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme
- Time-Splitting Schemes for Fractional Differential Equations I: Smooth Solutions
- Effective dynamics for boson stars
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT
- Dimension Reduction of the Schrödinger Equation with Coulomb and Anisotropic Confining Potentials
- A Bloch Decomposition–Based Split‐Step Pseudospectral Method for Quantum Dynamics with Periodic Potentials
- A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates
- Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub‐diffusion equations
This page was built for publication: On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross–Pitaevskii equations
