Fourth-order numerical methods for the coupled Korteweg–de Vries equations

Authors

  • Igor Korostil The Kirby Institute, University of New South Wales
  • Simon Clarke Monash University

DOI:

https://doi.org/10.21914/anziamj.v56i0.8630

Keywords:

coupled Korteweg–de Vries equations, numerical methods, exponential integrators, implicit Runge–Kutta method

Abstract

We compare six fixed-stepsize fourth-order numerical methods for a number of test problems described by a system of coupled Korteweg–de Vries equations. Particular attention is paid to the ability of these methods to preserve fixed points (solitary waves) and the invariants of the system, and establishing to what extent the conservation of integral invariants is indicative of the solution error for these methods. doi: 10.1017/S1446181115000012

Published

2015-04-12

Issue

Section

Articles for Printed Issues