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Symmetric linear multistep methods for Hamiltonian systems on manifolds

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Defense Thèse de doctorat : Univ. Genève, 2013 - Sc. 4591 - 2013/09/04
Abstract The aim of this work is the study of symmetric linear multistep methods applied to Hamiltonian systems; we show that this class of methods can have good properties of near preservation of the energy and momenta for long-time integrations of Hamiltonian systems. In Chapter 1 and 2 we study partitioned linear multistep methods applied to first order Hamiltonian equations, and we show how the use of symmetric partitioned multistep method can lead to near preservation of energy for a specific class of separable Hamiltonians. In Chapter 3, 4 and 5 we study symmetric linear multistep methods applied to second order constrained Hamiltonian systems. In Chapter 3 and 4 we focus on the theoretical analysis of the excellent behaviour that this class of methods presents on this kind of problems; we show as well the construction of these methods, and some numerical experiments. In Chapter 5 we study the optimization of the implementation of this class of methods.
Keywords Numerical AnalysisOrdinary Differential EquationsHamiltonian SystemConstrained Hamiltonian SystemsMultistep Methods
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URN: urn:nbn:ch:unige-302791
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CONSOLE, Paola. Symmetric linear multistep methods for Hamiltonian systems on manifolds. Université de Genève. Thèse, 2013. https://archive-ouverte.unige.ch/unige:30279

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Deposited on : 2013-10-07

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