Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
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.