ABSTRACT
Our objective, in this article, is to investigate the nonlinear Galerkin method with variable modes for the two-dimensional Kuramoto–Sivashinsky (K-S) equations. Complicated computing formulas of this method and those of some other related methods are carefully derived. Numerical computation of examples shows the efficiency and advantage of our method over the usual nonlinear Galerkin method and the classical Galerkin method. The computational efficiency confirms the theoretical results.
