On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations

Abstract

We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.

Functional‐preserving predictor‐corrector multiderivative schemes

“…The relaxation approach is not restricted to invariants and has also been extended to general functionals 𝜂 in refs. [16][17][18], resulting for example in efficient, fully-discrete, and locally entropy-stable numerical methods for computational fluid dynamics [21] and nonlinear dispersive wave equations [22][23][24].…”