A FULLY DISCRETE LOW-REGULARITY INTEGRATOR FOR THE KORTEWEG-DE VRIES EQUATION

In this paper we propose a fully discrete low-regularity integrator for the Korteweg-de Vries equation on the torus. This is an explicit scheme and can be computed with a complexity of O(NlogN) operations by fast Fourier transform, where N is the degrees of freedom in the spatial discretization. We prove that the scheme is first-order convergent in both time and space variables in H gamma-norm for H gamma +1 initial data under Courant-Friedrichs-Lewy condition N >= 1/tau, where tau denotes the temporal step size. We also carry out numerical experiments that illustrate the convergence behavior.