Variational integrators on fractional Lagrangian systems in the framework of discrete embedddings

Details Variational integrators on fractional Lagrangian systems in the framework of discrete embedddings Variational integrators on fractional Lagrangian systems in the framework of discrete embedddings

2011-03-02

arxiv.org/abs/1103.0465v1

Mathematics

Dynamical Systems

20 pages

Scientific paper

In this paper, we introduce the notion of discrete embedding which is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. We first define the Gauss finite differences embedding. In this setting, we study variational integrator on classical Lagrangian systems. Finally, we extend these constructions to the fractional case. In particular, we define the Gauss Gr\"unwald-Letnikov embedding and the corresponding variational integrator on fractional Lagrangian systems.

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