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

A fully discrete and fully explicit low-regularity integrator is constructed for the one-dimensional periodic cubic nonlinear Schrodinger 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 $$O(\tau \sqrt{\ln (1/\tau )}+N^{-1})$$ for $$H^1$$ initial data, without requiring any CFL condition, where $$\tau $$ and N denote the temporal stepsize and the degree of freedoms in the spatial discretisation, respectively.