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

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