A Fully Discrete Low-Regularity Integrator for the Nonlinear Schrodinger Equation

For the solution of the one dimensional cubic nonlinear Schrodinger equation on the torus, we propose and analyze a fully discrete low-regularity integrator. The considered scheme is explicit. Its implementation relies on the fast Fourier transform with a complexity of O(N log N) operations per time step, where N denotes the degrees of freedom in the spatial discretization. We prove that the newscheme provides anO(tau(3/2 gamma-1/2-epsilon)+N-gamma) error bound in L-2 for any initial data in H-gamma, 1/2 < gamma <= 1, where tau denotes the temporal step size. Numerical examples illustrate this convergence behavior.