A time-splitting Galerkin finite element method for the Davey–Stewartson equations

Abstract

In this paper, we propose a time-splitting Galerkin method to investigate the evolution of the Davey–Stewartson equations. Using time-splitting, we split the nonlinear equations into two subequations: a linear equation and a nonlinear equation. The nonlinear equation is directly solved and the linear equation is approximated by Galerkin finite element. The error norms and conservation variables of four numerical experiments illustrate the efficiency and accuracy of our numerical scheme.