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Numerical methods for curve evolution under dispersive geometric dynamics
Abstract
In this thesis, I present non-stiff pseudo-spectral methods to study 2-D curves that follow dispersive geometric evolution laws under Euclidean and Affine geometries. Specifically, I present numerical solutions for Airy flow and Central Affine flow. This includes the periodic solutions of Korteweg de Vries equation (KdV) and its first nonlinear generalization (mKdV) from the corresponding curvatures of the 2-D curves; a fully discrete space-time analysis of the equations and numerical evidence that confirms the accuracy, convergence, efficiency, and stability of the methods.