An efficient time-splitting compact finite difference method for Gross-Pitaevskii equation

DOI10.1016/j.amc.2016.10.037zbMath1411.65116OpenAlexW2542295476MaRDI QIDQ1735071

Wen Gao, Hanquan Wang, Xiu Ma, Jun-Liang Lu

Publication date: 28 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2016.10.037

zbMATH Keywords

Gross-Pitaevskii equationcompact finite difference methodtime-splittingnonlinear Schrödinger-type equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

An efficient split-step compact finite difference method for the coupled Gross–Pitaevskii equations, An efficient high-order compact finite difference method for the Helmholtz equation, A new compact alternating direction implicit method for solving two dimensional time fractional diffusion equation with Caputo-Fabrizio derivative, A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions, Error bounds of fourth‐order compact finite difference methods for the Dirac equation in the massless and nonrelativistic regime, A second-order fast compact scheme with unequal time-steps for subdiffusion problems, Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation, Split-step cubic B-spline collocation methods for nonlinear Schrödinger equations in one, two, and three dimensions with Neumann boundary conditions, Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions, Conservative finite-difference scheme for the 2D problem of femtosecond laser pulse interaction with kink structure of high absorption in semiconductor

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations
• Optimal \(l^\infty\) error estimates of finite difference methods for the coupled Gross-Pitaevskii equations in high dimensions
• A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
• An efficient Chebyshev-tau spectral method for Ginzburg-Landau-Schrödinger equations
• Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation
• Fourth-order compact solution of the nonlinear Klein-Gordon equation
• Compact high-order schemes for the Euler equations
• A numerical scheme for the nonlinear Schrödinger equation
• Compact finite difference schemes with spectral-like resolution
• Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
• High-order finite-difference schemes for numerical simulation of hypersonic boundary-layer transition
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Fractional step methods for parabolic equations with a non-standard condition
• Numerical solution of the three-dimensional advection--diffusion equation.
• A new ADI technique for two-dimensional parabolic equation with an integral condition
• On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
• Mathematical theory and numerical methods for Bose-Einstein condensation
• An efficient implementation of fourth-order compact finite difference scheme for Poisson equation with Dirichlet boundary conditions
• A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrödinger equation
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• Numerical simulation of singular solutions to the two-dimensional cubic schrödinger equation
• Time‐splitting procedures for the solution of the two‐dimensional transport equation
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• Higher Order Compact Implicit Schemes for the Wave Equation
• Nonlinearly Stable Compact Schemes for Shock Calculations
• High‐order compact scheme for the steady stream‐function vorticity equations
• Optimal Error Estimates of Compact Finite Difference Discretizations for the Schrödinger-Poisson System