Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg-Landau equations. (English) Zbl 1414.65026
Summary: In this paper, we discuss the error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex space fractional Ginzburg-Landau equations. The continuous mass and energy inequalities as well as their discrete versions are presented. Moreover, by the discrete mass and energy inequalities, the error estimate of the Fourier pseudo-spectral scheme is established, and the scheme is proved to have the spectral accuracy.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35Q56 | Ginzburg-Landau equations |
| 35R11 | Fractional partial differential equations |
Keywords:
multidimensional fractional Ginzburg-Landau equation; Fourier pseudo-spectral method; discrete mass and energy inequalities; error estimateReferences:
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