Implicit-explicit multistep methods for general two-dimensional nonlinear Schroedinger equations

摘要

In this paper, implicit-explicit multistep Galerkin methods are studied for two-dimensional nonlinear Schrodinger equations and coupled nonlinear Schrodinger 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 L_2 and L_∞ norm can be reached.