An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg-Landau equations

DOI10.1016/j.camwa.2017.12.005zbMath1409.65057OpenAlexW2781767258MaRDI QIDQ1732484

Nan Wang, Cheng-Ming Huang

Publication date: 25 March 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.12.005

zbMATH Keywords

convergenceRiesz fractional derivativesplit-stepfractional Ginzburg-Landau equationquasi-compact method

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) Fractional partial differential equations (35R11)

Related Items (21)

A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations ⋮ The construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I) ⋮ A Fast Compact Difference Method for Two-Dimensional Nonlinear Space-Fractional Complex Ginzburg-Landau Equations ⋮ Well-posedness of space fractional Ginzburg-Landau equations involving the fractional Laplacian arising in a Bose-Einstein condensation and its kernel based approximation ⋮ Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation ⋮ Exponential Runge-Kutta method for two-dimensional nonlinear fractional complex Ginzburg-Landau equations ⋮ Fast TT-M fourth-order compact difference schemes for a two-dimensional space fractional Gray-Scott model ⋮ Dissipation-preserving Galerkin-Legendre spectral methods for two-dimensional fractional nonlinear wave equations ⋮ The construction of an optimal fourth-order fractional-compact-type numerical differential formula of the Riesz derivative and its application ⋮ High-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation ⋮ A meshless approach for solving nonlinear variable-order time fractional 2D Ginzburg-Landau equation ⋮ Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain ⋮ A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg-Landau equations ⋮ Fast iterative solvers for the two-dimensional spatial fractional Ginzburg-Landau equations ⋮ Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg-Landau equations ⋮ New exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation via the conformable fractional derivative ⋮ Vieta-Lucas polynomials for the coupled nonlinear variable-order fractional Ginzburg-Landau equations ⋮ Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation ⋮ High-dimensional nonlinear Ginzburg-Landau equation with fractional Laplacian: discretization and simulations ⋮ Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation ⋮ A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Point-wise error estimate of a conservative difference scheme for the fractional Schrödinger equation
• Maximum-norm error analysis of a difference scheme for the space fractional CNLS
• A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• An efficient fully linearized semi-implicit Galerkin-mixed FEM for the dynamical Ginzburg-Landau equations of superconductivity
• Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative
• An efficient split-step compact finite difference method for cubic-quintic complex Ginzburg-Landau equations
• Galerkin finite element method for nonlinear fractional Schrödinger equations
• 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
• A fourth-order approximation of fractional derivatives with its applications
• An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Some applications of fractional equations.
• Chaos, fractional kinetics, and anomalous transport
• Finite difference approximations for fractional advection-dispersion flow equations
• 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
• Fractional diffusion on bounded domains
• Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation
• A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations
• On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres
• Riesz fractional derivatives and fractional dimensional space
• 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
• Galerkin finite element method for the nonlinear fractional Ginzburg-Landau equation
• Fast iterative method with a second-order implicit difference scheme for time-space fractional convection-diffusion equation
• Fractional generalization of the Ginzburg-Landau equation: an unconventional approach to critical phenomena in complex media
• Convergence analysis of a linearized Crank-Nicolson scheme for the two-dimensional complex Ginzburg-Landau equation
• A linearized high-order difference scheme for the fractional Ginzburg-Landau equation
• The world of the complex Ginzburg-Landau equation
• Fractional dynamics of coupled oscillators with long-range interaction
• A Linearized Crank-Nicolson-Galerkin Method for the Ginzburg-Landau Model
• Spectral Methods in MATLAB
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• Fourth Order Difference Approximations for Space Riemann-Liouville Derivatives Based on Weighted and Shifted Lubich Difference Operators
• ASYMPTOTIC DYNAMICS OF 2D FRACTIONAL COMPLEX GINZBURG–LANDAU EQUATION
• Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation
• On the Construction and Comparison of Difference Schemes

This page was built for publication: An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg-Landau equations