A NONLINEAR GALERKIN METHOD WITH VARIABLE MODES FOR KURAMOTO-SIVASHINSKY EQUATION

This article proposes a kind of nonlinear Galerkin methods with variable modesfor the long-term integration of Kuramoto-Sivashinsky equation. It consists offinding an appropriate or best number of modes in the correction of the method.Convergence results and error estimates are derived for this method. Numericalexamples show also the efficiency and advantage of our method over the usualnonlinear Galerkin method and the classical Galerkin method.