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In this paper, the coupled space fractional Ginzburg–Landau equations are investigated numerically. A linearized semi-implicit difference scheme is proposed. The scheme is unconditionally stable, fourth-order accurate in space, and second-order accurate in time. The optimal pointwise error estimates, unique solvability, and unconditional stability are obtained. Moreover, Richardson extrapolation is exploited to improve the temporal accuracy to fourth order. Finally, numerical results are presented to confirm the theoretical results.

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