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In this paper, we first construct a linearized Galerkin‐Legendre spectral method for the one‐dimensional nonlinear fractional Ginzburg‐Landau equation, where a three‐level linearized Crank‐Nicolson scheme is used for time discretization. The unique solvability and boundedness properties of the fully discrete scheme are analyzed. It is shown that the method is unconditionally convergent in the maximum...
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