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

01/11/2021

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by   Buyang Li, et al.

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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 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.