ERROR ESTIMATES OF THE SPECTRAL COLLOCATION METHOD FOR THE GINZBURG-LANDAU EQUATION COUPLED WITH THE BENJAMIN-BONA-MAHONY EQUATION

摘要

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.