Order estimates in time of splitting methods for the nonlinear Schrödinger equation

Abstract

In this paper, we consider the nonlinear Schrödinger equation $u_t + i\Delta u − F(u) = 0$ in two dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang formulae (which are splitting methods) are approximations of the exact solution of order 1 and 2 in time.