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In this paper, we consider the spectral collocation method for the Ginzburg–Landau equation coupled with the Benjamin–Bona–Mahony equation. Semidiscrete and fully discrete spectral collocation schemes are given. In the fully discrete case, a three-level spectral collocation scheme is considered. An energy estimation method is used to obtain error estimates for the approximate solutions.

Error estimates of the spectral collocation method for the Ginzburg–Landau equation coupled with the Benjamin–Bona–Mahony equation