Non-stiff methods for Airy flow and the modified Korteweg-de Vries equation
Numerical Analysis
2017-08-31 v1
Abstract
In this paper, we implement non-stiff interface tracking methods for the evolution of 2-D curves that follow Airy flow, a curvature-dependent dispersive geometric evolution law. The curvature of the curve satisfies the modified Korteweg-de Vries equation, a dispersive non-linear soliton equation. We present a fully discrete space-time analysis of the equations (proof of convergence) and numerical evidence that confirms the accuracy, convergence, efficiency, and stability of the methods.
Keywords
Cite
@article{arxiv.1708.09154,
title = {Non-stiff methods for Airy flow and the modified Korteweg-de Vries equation},
author = {Mariano Franco-de-León and John Lowengrub},
journal= {arXiv preprint arXiv:1708.09154},
year = {2017}
}
Comments
39 pages, 40 figures