Stability analysis of nonlinear galerkin & galerkin methods for nonlinear evolution equations

Abstract

Our object in this article is to describe the Galerkin scheme and nonlinear Galerkin scheme for the approximation of nonlinear evolution equations, and to study the stability of these schemes. Spatial discretization can be performed by either Galerkin spectral method or nonlinear Galerkin spectral method; time discretization is done by Euler scheme which is explicit or implicit in the nonlinear terms. According to the stability analysis of the above schemes, the stability of nonlinear Galerkin method is better than that of Galerkin method.