Non-stiff methods for Airy flow and the modified Korteweg-de Vries equation
Provides a provably convergent numerical framework for a dispersive geometric flow, benefiting researchers in geometric PDEs and soliton dynamics.
The paper develops non-stiff numerical methods for simulating Airy flow, a geometric evolution law, and proves their convergence. Numerical experiments confirm accuracy and efficiency.
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.