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