Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schrödinger equation

DOI10.1016/j.apnum.2018.10.012zbMath1407.65230OpenAlexW2899878741MaRDI QIDQ1633330

Y. Aharonov

Publication date: 19 December 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.10.012

zbMATH Keywords

mass conservationspectral Galerkin methodsplit-step methodmatrix diagonalization methodtwo-dimensional nonlinear space-fractional Schrödinger equation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

Related Items (27)

A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations ⋮ A linearized conservative Galerkin-Legendre spectral method for the strongly coupled nonlinear fractional Schrödinger equations ⋮ Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation ⋮ High-order structure-preserving algorithms for the multi-dimensional fractional nonlinear Schrödinger equation based on the SAV approach ⋮ A novel alternating-direction implicit spectral Galerkin method for a multi-term time-space fractional diffusion equation in three dimensions ⋮ Implicit Runge-Kutta and spectral Galerkin methods for Riesz space fractional/distributed-order diffusion equation ⋮ Hamiltonian-preserving schemes for the two-dimensional fractional nonlinear Schrödinger wave equations ⋮ Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations ⋮ A Linearly-Implicit Energy-Preserving Algorithm for the Two-Dimensional Space-Fractional Nonlinear Schrödinger Equation Based on the SAV Approach ⋮ On the L^∞ convergence of a conservative Fourier pseudo‐spectral method for the space fractional nonlinear Schrödinger equation ⋮ Two novel conservative exponential relaxation methods for the space-fractional nonlinear Schrödinger equation ⋮ An accelerated novel meshless coupled Algorithm for non-local nonlinear behavior in 2D/3D space-fractional GPEs ⋮ High-order schemes for the fractional coupled nonlinear Schrödinger equation ⋮ Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations ⋮ A split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger equations ⋮ High-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation ⋮ Convergence of an energy-conserving scheme for nonlinear space fractional Schrödinger equations with wave operator ⋮ A linear, symmetric and energy-conservative scheme for the space-fractional Klein-Gordon-Schrödinger equations ⋮ The inverse problem and the second order \(\theta\) scheme with finite element method used for 2D nonlinear space fractional Schrödinger equation ⋮ An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation ⋮ On convergence of a structure preserving difference scheme for two-dimensional space-fractional nonlinear Schrödinger equation and its fast implementation ⋮ Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation ⋮ Numerical analysis of fractional viscoelastic column based on shifted Chebyshev wavelet function ⋮ Efficient energy preserving Galerkin-Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator ⋮ A linear finite difference scheme for the two-dimensional nonlinear Schrödinger equation with fractional Laplacian ⋮ Structure preserving fourth-order difference scheme for the nonlinear spatial fractional Schrödinger equation in two dimensions ⋮ Dynamic analysis of variable fractional order cantilever beam based on shifted Legendre polynomials algorithm

Cites Work

• Unnamed Item
• Unnamed Item
• High-order algorithms for Riesz derivative and their applications. III
• Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations
• Maximum-norm error analysis of a difference scheme for the space fractional CNLS
• An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations
• Numerical algorithm for the variable-order Caputo fractional functional differential equation
• A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations
• High-order algorithms for Riesz derivative and their applications. II
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• Galerkin finite element method for nonlinear fractional Schrödinger equations
• Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars
• The global solution for a class of systems of fractional nonlinear Schrödinger equations with periodic boundary condition
• A high-accuracy preserving spectral Galerkin method for the Dirichlet boundary-value problem of variable-coefficient conservative fractional diffusion equations
• Spectral direction splitting methods for two-dimensional space fractional diffusion equations
• Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
• Fractional quantum mechanics and Lévy path integrals
• High-order algorithms for Riesz derivative and their applications. I.
• Finite difference approximations for fractional advection-dispersion flow equations
• On the continuum limit for discrete NLS with long-range lattice interactions
• Error analysis of the Strang time-splitting Laguerre-Hermite/Hermite collocation methods for the Gross-Pitaevskii equation
• Quasi-compact finite difference schemes for space fractional diffusion equations
• Split-step alternating direction implicit difference scheme for the fractional Schrödinger equation in two dimensions
• Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
• Well-posedness for the nonlinear fractional Schrödinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation
• A conservative linearized difference scheme for the nonlinear fractional Schrödinger equation
• Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
• A class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations
• Bound state for the fractional Schrödinger equation with unbounded potential
• Soliton dynamics for fractional Schrödinger equations
• Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
• An Intuitive Study of Fractional Derivative Modeling and Fractional Quantum in Soft Matter
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd
• Some physical applications of fractional Schrödinger equation
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• A class of second order difference approximations for solving space fractional diffusion equations
• Ground state solutions of asymptotically linear fractional Schrödinger equations
• Variational formulation for the stationary fractional advection dispersion equation
• A linearly implicit conservative scheme for the fractional nonlinear Schrödinger equation with wave operator

This page was built for publication: Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schrödinger equation