Discrete Conservative Vector Fields Induced by the Trapezoidal Method

Date of Online Publication: 26/08/2006
Keywords: Conservative vector elds, Hamiltonian systems, symplecticity, symmetric methods
Authors: Felice Iavernaro and Donato Trigiante
Pages: 113-130
The use of symmetric schemes has revealed interesting stability properties for the long time simulation of conservative, and in particular Hamiltonian systems. By using one of the simplest symmetric formulae, namely the trapezoidal method, we show that, under certain circumstances, one can attach to the discrete system a discrete energy function and therefore obtain a discrete conservative dynamical system.

 

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