This paper aims to investigate the stability and numerical approximation of Sivashinsky equations. We can extend a stability theorem on the higher order elliptic equation such as biharmonic equation by the eigenfunction expansion. Because RBFs do not generally vanish on the boundary, they can not directly approximate a Dirichlet boundary problem by Galerkin method. An auxiliary parametrized technique is used to convert a Dirichlet boundary condition to a Robin one. We apply the Galerkin meshfree method based on radial basis functions to discretize the spatial variables and use a group presenting scheme for the time discretization. Some experimental results will be presented to show the performance of the proposed method
