An efficient spectral-collocation difference method for two-dimensional Schrödinger equation with Neumann boundary conditions
DOI10.1016/j.camwa.2019.11.006zbMath1437.65214OpenAlexW2990528228MaRDI QIDQ2179055
Publication date: 12 May 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2019.11.006
conservation lawsNeumann boundary conditionsSchrödinger equationfast algorithmdiscrete cosine transformspectral-collocation
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for discrete and fast Fourier transforms (65T50) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
- An efficient spectral method for computing dynamics of rotating two-component Bose-Einstein condensates via coordinate transformation
- Jacobi spectral method with essential imposition of Neumann boundary condition
- The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional nonlinear Schrödinger equation
- Pseudo-spectral solution of nonlinear Schrödinger equations
- Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
- High-order time-splitting Hermite and Fourier spectral methods
- On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
- Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation
- Local discontinuous Galerkin methods for nonlinear Schrödinger equations
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
- Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
- \(B\)-spline finite element studies of the nonlinear Schrödinger equation
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation
- Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
- Implementation of Neumann boundary condition with influence matrix method for viscous annular flow using pseudospectral collocation
- A spectral method for elliptic equations: The Neumann problem
- Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
- Compact difference schemes for heat equation with Neumann boundary conditions (II)
- A Generalized-Laguerre–Fourier–Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose–Einstein Condensates
- High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations
- Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method
- Numerical solution to the unsteady two-dimensional Schrödinger equation using meshless local boundary integral equation method
- A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
- On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation
- On the finite-differences schemes for the numerical solution of two dimensional Schrödinger equation
- Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation
- Fourth‐order compact schemes of a heat conduction problem with Neumann boundary conditions
- Fourth‐order compact schemes for solving multidimensional heat problems with Neumann boundary conditions
- Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation
- A fourth-order compact algorithm for nonlinear reaction-diffusion equations with Neumann boundary conditions
- A Fourth-Order Time-Splitting Laguerre--Hermite Pseudospectral Method for Bose--Einstein Condensates