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A linear discrete scheme for the Ginzburg-Landau equation. (English) Zbl 1145.65081

The authors consider the Ginzburg-Landau nonlinear evolution equation with a periodic initial condition. A discrete Galerkin-Fourier approximation scheme is analyzed. The existence and convergence of global attractors are obtained. The convergence and error estimates of the discrete solution are shown.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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References:

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