A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation - Li, Buyang; Wu, Yifei (Numerische Mathematik, 2021)
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 ( N ln N ) operations at every time level, and is proved to have an L 2 -norm error bound of O ( τ ln ( 1 / τ ) + N - 1 ) for H 1 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.