Affiliation:
1. University of Innsbruck, 6020 Innsbruck, Austria
Abstract
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 for solutions in the Sobolev space $H^3((-\pi , \pi ))$, respectively. Numerical examples illustrating our convergence result are given.
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,General Mathematics
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