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The string method is an efficient numerical method for finding transition paths and transition rates in metastable systems. The dynamics of the string are governed by a HamiltonJacobi type of equation. We construct a stable and high order numerical scheme to estimate the first order spatial derivatives, or the tangent vectors in the equation. The construction is based on the idea of the upwind scheme and the essentially nonoscillatory scheme (ENO). Numerical examples demonstrate the improvement of the accuracy by the new scheme.

Higher Order String Method for Finding Minimum Energy Paths