Error propagation in the numerical integration of solitary waves. The regularized long wave equation

Abstract

We study the error propagation of time integrators of solitary wave solutions for the regularized long wave equation, u t+u x+ 1 2 (u 2) x−u xxt=0 , by using a geometric interpretation of these waves as relative equilibria. We show that the error growth is linear for schemes that preserve invariant quantities of the problem and quadratic for ‘nonconservative’ methods. Numerical experiments are presented.