A Lawson-type exponential integrator for the Korteweg–de Vries equation
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 $\tau$ …