Implicit–explicit multistep methods for general two-dimensional nonlinear Schrödinger equations

In this paper, implicit–explicit multistep Galerkin methods are studied for two-dimensional nonlinear Schrödinger equations and coupled nonlinear Schrödinger equations. The spatial discretization is based on Galerkin method using linear and quadratic basis functions on triangular and rectangular finite elements. And the implicit–explicit multistep method is used for temporal discretization. Linear and nonlinear numerical tests are presented to verify the validity and efficiency of the numerical methods. The numerical results record that the optimal order of the error in L₂ and L_∞ norm can be reached.