On splitting methods for Schrodinger-Poisson and cubic nonlinear Schrodinger equations

We give an error analysis of Strang-type splitting integrators for nonlinear Schrodinger equations. For Schrodinger-Poisson equations with an H-4-regular solution, a first-order error bound in the H-1 norm is shown and used to derive a second-order error bound in the L-2 norm. For the cubic Schrodinger equation with an H-4-regular solution first-order convergence in the H-2 norm is used to obtain second-order convergence in the L-2 norm. Basic tools in the error analysis are Lie-commutator bounds for estimating the local error and H-m-conditional stability for error propagation, where m = 1 for the Schrodinger-Poisson system and m = 2 for the cubic Schrodinger equation.