Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain

DOI10.1016/j.aml.2020.106710zbMath1453.65365OpenAlexW3080088892WikidataQ115597787 ScholiaQ115597787MaRDI QIDQ2213693

Pengde Wang

Publication date: 3 December 2020

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

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106710

zbMATH Keywords

exponential time differencingfractional Laplacianspectral-Galerkin methodfractional Ginzburg-Landau equationmapped Chebyshev functions

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Fractional partial differential equations (35R11) Ginzburg-Landau equations (35Q56)

Related Items (10)

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) ⋮ Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain ⋮ Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation ⋮ High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation ⋮ Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg-Landau equation with Caputo derivative ⋮ Application of Pell collocation method for solving the general form of time-fractional Burgers equations ⋮ High-order numerical algorithm and error analysis for the two-dimensional nonlinear spatial fractional complex Ginzburg-Landau equation ⋮ Fast iterative solvers for the two-dimensional spatial fractional Ginzburg-Landau equations ⋮ A linearized element-free Galerkin method for the complex Ginzburg-Landau equation

Cites Work

• Fourier spectral approximations to the dynamics of 3D fractional complex Ginzburg-Landau equation
• Exponential time differencing for stiff systems
• An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
• An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg-Landau equations
• Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg-Landau equations
• An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation
• An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation
• Exponential Runge-Kutta method for two-dimensional nonlinear fractional complex Ginzburg-Landau equations
• Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation
• Galerkin finite element method for the nonlinear fractional Ginzburg-Landau equation
• Fractional generalization of the Ginzburg-Landau equation: an unconventional approach to critical phenomena in complex media
• A linearized high-order difference scheme for the fractional Ginzburg-Landau equation
• The world of the complex Ginzburg-Landau equation
• An efficient difference scheme for the coupled nonlinear fractional Ginzburg–Landau equations with the fractional Laplacian
• Fast Fourier-like Mapped Chebyshev Spectral-Galerkin Methods for PDEs with Integral Fractional Laplacian in Unbounded Domains
• Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains
• Hermite Spectral Methods for Fractional PDEs in Unbounded Domains

This page was built for publication: Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain