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 $O(N\ln N)$ 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.

References in corpus (4)

• Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
• Low-regularity integrators for nonlinear Dirac equations
• Optimal convergence of a second order low-regularity integrator for the KdV equation
• Embedded exponential-type low-regularity integrators for KdV equation under rough data

Cited by in corpus (2)

• Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn equation
• A semi-implicit low-regularity integrator for Navier-Stokes equations