Error estimates of second-order BDF Galerkin finite element methods for a coupled nonlinear Schrödinger system

Abstract

This paper aims to study two kinds of second-order BDF finite element schemes for a coupled nonlinear Schrödinger system. The proposed schemes are semi-implicit schemes where nonlinear terms are linearized by the implicit-explicit method and explicit method, respectively. We prove that error estimates in L 2 -norm are unconditionally optimal which means that there is no restriction of the time step and mesh size. Finally, numerical results are given to illustrate theoretical analysis.