A Lawson-type exponential integrator for the Korteweg-de Vries equation

Abstract

We propose an explicit numerical method for the periodic Korteweg-de Vries equation. Our method is based on a Lawson-type exponential integrator for time integration and the Rusanov scheme for Burgers' nonlinearity. We prove first-order convergence in both space and time under a mild Courant-Friedrichs-Lewy condition $τ=O(h)$, where $τ$ and $h$ represent the time step and mesh size, respectively. Numerical examples illustrating our convergence result are given.