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On Yoshida's Method For Constructing Explicit Symplectic Integrators For Separable Hamiltonian Systems

Pim, Jonathan (2019) On Yoshida's Method For Constructing Explicit Symplectic Integrators For Separable Hamiltonian Systems. Bachelor's Thesis, Mathematics.

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Abstract

We describe Yoshida's method for separable Hamiltonians $H = T(p)+V(q)$. Hamiltonians of this form occur frequently in classical mechanics, for example the $n$-body problem, as well as in other fields. The class of symplectic integrators constructed are explicit, reversible, of arbitrary even order, and have bounded energy growth. We give an introduction to Hamiltonian mechanics, symplectic geometry, and Lie theory. We compare the performance of these integrators to more commonly used methods such as Runge-Kutta, using the ideal pendulum and Kepler problem as examples.

Item Type: Thesis (Bachelor's Thesis)
Supervisor:
Supervisor nameSupervisor E mail
Seri, M.M.Seri@rug.nl
Sterk, A.E.A.E.Sterk@rug.nl
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 12 Jul 2019
Last Modified: 17 Jul 2019 09:56
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/20185

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