On the numerical accuracy of the method of multiple scales for nonlinear dispersive wave equations
Numerical Analysis
2021-03-29 v1 Numerical Analysis
Pattern Formation and Solitons
Computational Physics
Abstract
In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and the complex nature of the time-frequency. The MMS is tested as an initial value problem using three choices of the dispersion model, one toy and two Lorentz models. Depending on the parameters of the problem, the amplitude equation can be both well- or ill-posed. Despite the ill-posedness, the MMS solution remains a valid approximation of the solution to the original nonlinear model.
Keywords
Cite
@article{arxiv.2103.14437,
title = {On the numerical accuracy of the method of multiple scales for nonlinear dispersive wave equations},
author = {David Juhasz and Per Kristen Jakobsen},
journal= {arXiv preprint arXiv:2103.14437},
year = {2021}
}