A mass‐ and energy‐preserving numerical scheme for solving coupled Gross–Pitaevskii equations in high dimensions

DOI10.1002/NUM.23042OpenAlexW4378231720MaRDI QIDQ6071351

Ting-chun Wang, Jianfeng Liu, Qinglin Tang

Publication date: 23 November 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.23042

zbMATH Keywords

finite difference methodsolvabilitycoupled Gross-Pitaevskii equationsmass and energy conservationpoint-wise error estimate

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

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• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• Optimal point-wise error estimate of a compact difference scheme for the coupled Gross-Pitaevskii equations in one dimension
• Optimal \(l^\infty\) error estimates of finite difference methods for the coupled Gross-Pitaevskii equations in high dimensions
• The multisymplectic numerical method for Gross-Pitaevskii equation
• A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• A characteristic-Galerkin approximation to a system of shallow water equations
• Unconditional and optimal \(H^2\)-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions
• Functionally-fitted energy-preserving integrators for Poisson systems
• High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations
• An efficient time-splitting compact finite difference method for Gross-Pitaevskii equation
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs
• Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation
• A time-splitting spectral method for coupled Gross-Pitaevskii equations with applications to rotating Bose-Einstein condensates
• An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates
• Ground, symmetric and central vortex states in rotating Bose-Einstein condensates
• Berry phase effects on electronic properties
• A Generalized-Laguerre–Fourier–Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose–Einstein Condensates
• Global well posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions
• Finite Element Approximations to the System of Shallow Water Equations, Part II: Discrete-Time A Priori Error Estimates
• Highly accurate finite difference method for coupled nonlinear Schrödinger equation
• Finite Difference Method for Generalized Zakharov Equations
• Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
• High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
• Unconditionally Bound Preserving and Energy Dissipative Schemes for a Class of Keller--Segel Equations
• Ground States and Dynamics of Spin-Orbit-Coupled Bose--Einstein Condensates
• Global well posedness for the Gross–Pitaevskii equation with an angular momentum rotational term
• Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation
• The Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic Potential
• Numerical simulation of coupled nonlinear Schrödinger equation

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