A fourth-order linearized difference scheme for the coupled space fractional Ginzburg–Landau equation

Yuan, Xu; Zeng, Jianhua; Hu, Shuanggui

doi:10.1186/s13662-019-2389-5

Cited by 4 publications

(1 citation statement)

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“…There exists a wide variety of numerical methods which deal with space and/or fractional differential equations [24][25][26][27][28][29][30][31]. The coupled space fractional Ginzburg-Landau system was numerically investigated in [32]. A linearized semi-implicit difference scheme is proposed with unconditional stability and fourth order of convergence.…”

Section: Introductionmentioning

confidence: 99%

Alikhanov Legendre—Galerkin Spectral Method for the Coupled Nonlinear Time-Space Fractional Ginzburg–Landau Complex System

2021

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A finite difference/Galerkin spectral discretization for the temporal and spatial fractional coupled Ginzburg–Landau system is proposed and analyzed. The Alikhanov L2-1σ difference formula is utilized to discretize the time Caputo fractional derivative, while the Legendre-Galerkin spectral approximation is used to approximate the Riesz spatial fractional operator. The scheme is shown efficiently applicable with spectral accuracy in space and second-order in time. A discrete form of the fractional Grönwall inequality is applied to establish the error estimates of the approximate solution based on the discrete energy estimates technique. The key aspects of the implementation of the numerical continuation are complemented with some numerical experiments to confirm the theoretical claims.

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