Spectral splitting method for nonlinear Schrödinger equations with quadratic potential

•We give an approximate solution to nonlinear Schrödinger equations.•We separately treat the linear Schrödinger equation and the nonlinear term.•We give a precise estimate of the remainder term.•We compare the modified spectral splitting approximation with the standard one. In this paper we propose a modified Lie-type spectral splitting approximation where the external potential is of quadratic type. It is proved that we can approximate the solution to a one-dimensional nonlinear Schrödinger equation by solving the linear problem and treating the nonlinear term separately, with a rigorous estimate of the remainder term. Furthermore, we show by means of numerical experiments that such a modified approximation is more efficient than the standard one.