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 $\tau =O(h)$, where $\tau$ and $h$ represent the time step and mesh size, respectively. Numerical examples illustrating our convergence result are given.

17 pages, 4 figures

References in corpus (1)

• A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev--Petviashvili equation