The Evolution of Initial Small Disturbance in Discrete Computation of Contour Dynamics

Abstract

In this paper, we mainly discuss the evolution of initial small disturbance in discrete computation of the contour dynamics method. For one class of smooth contour, we prove the stability of evolution of initial small disturbance based on the analysis of the convergence of the contour dynamics method with Euler's explicit method in time. Namely, at terminal time T, the evolving disturbance is going to zero as initial small disturbance goes to zero. The numerical experiment on the stability of contour dynamics has been given in [5,6].