Description
In this talk we will be concerned with the Nonlinear Schrödinger Equations with Time-Dependent Potential. We will propose a new numerical method based on splitting in time and spectral method in space. Second order splitting will be obtained via linearisation combined with iterated Duhamel formula. In spectral discretization we will employ the basis of Hermite functions, for which we will present the exact, analytic expression of solution to the free Schrödinger equation.
