A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg-Landau equations
A three-level linearized finite difference method for the two-dimensional Riesz space-fractional complex nonlinear Ginzburg-Landau equations is studied. The paper is organized as follows. Section 1 is an introduction. In Section 2, some basic and useful lemmas are presented. The numerical scheme and the analysis of the the local truncation error is derived in Section 3. The uniqueness, boundedness, and convergence of the proposed three-level linearized method are given in this section too. In Section 4, a fast preconditioner for solving the resulting discretized complex linear system is proposed. In Section 5, some numerical examples with tables and graphical illustrations are given and analyzed. In Section 6, concluding remarks and some future works are drawn.
space fractional Ginzburg-Landau equation
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