Fourier spectral method with an adaptive time strategy for nonlinear fractional Schrödinger equation

DOI10.1002/num.22453OpenAlexW2995407348WikidataQ114235301 ScholiaQ114235301MaRDI QIDQ6071673

Zi-Hang She, Hai-Dong Qu

Publication date: 28 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.22453

zbMATH Keywords

fractional Schrödinger equationfractional Laplacian operatorFourier spectraladaptive time step

Mathematics Subject Classification ID

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

Related Items (1)

Fourier spectral method for a class of nonlinear Schrödinger models

Cites Work

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• Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
• Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative
• Galerkin finite element method for nonlinear fractional Schrödinger equations
• Exponential time differencing for stiff systems
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Numerical methods for the solution of partial differential equations of fractional order.
• Fractional quantum mechanics and Lévy path integrals
• \(L^{p}\) estimates for fractional Schrödinger operators with Kato class potentials
• A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
• Solitary wave solutions for nonlinear fractional Schrödinger equation in Gaussian nonlocal media
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Almost structure-preserving analysis for weakly linear damping nonlinear Schrödinger equation with periodic perturbation
• Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
• A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator
• Conformal conservation laws and geometric integration for damped Hamiltonian PDEs
• Well-posedness for the nonlinear fractional Schrödinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation
• Fast and stable explicit operator splitting methods for phase-field models
• Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
• Energy-conserving methods for the nonlinear Schrödinger equation
• Boson stars as solitary waves
• Spectral Methods
• An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
• Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method
• A Stochastic Model for Analysis of Longitudinal AIDS Data
• On structure preserving and circulant preconditioners for the space fractional coupled nonlinear Schrödinger equations
• Fractional kinetic equations: solutions and applications
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• Fourth-Order Time-Stepping for Stiff PDEs
• Numerical study of fractional nonlinear Schrödinger equations
• On finite time blow-up for the mass-critical Hartree equations
• Variable mesh difference schemes for solving a nonlinear Schrödinger equation with a linear damping term

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