Stability and convergence of the string method for computing minimum energy paths

2018/07/16 by Van Koten, Brian, Luskin, Mitchell
#65 #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1807.06094

Abstract

We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.

Related

• Modified string method for finding minimum energy path
• Stability of the Minimum Energy Path
• Convergence of the Discrete Minimum Energy Path
• A convergent string method: Existence and approximation for the Hamiltonian boundary-value problem
• A simple Chain-of-States method in acceleration space for the efficient location of Minimum Energy Paths