A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation

Abstract

A fully discrete and fully explicit low-regularity integrator is constructed for the one-dimensional periodic cubic nonlinear Schrödinger equation. The method can be implemented by using fast Fourier transform with O(Nln N) operations at every time level, and is proved to have an L2-norm error bound of O(τln(1/τ)+N-1) for H1 initial data, without requiring any CFL condition, where τ and N denote the temporal stepsize and the degree of freedoms in the spatial discretisation, respectively. [Formula not fully presented, refer to publisher pdf]