Abstract
A string method for the computation of Hamiltonian trajectories linking two given points is presented, based on the Maupertuis principle; trajectories then correspond to geodesics. For local geodesics, convergence of an algorithm based on Birkhoff’s method has been shown recently in Schwetlick and Zimmer (Submitted). We demonstrate how to extend this approach to global geodesics and thus arbitrary boundary values of the corresponding Hamiltonian problem. Numerical illustrations of the algorithm are given, as well as situations are shown in which the method converges to a degenerate solution.
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Schwetlick, H., Zimmer, J. (2013). The Computation of Long Time Hamiltonian Trajectories for Molecular Systems via Global Geodesics. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_25
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DOI: https://doi.org/10.1007/978-3-642-33134-3_25
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