Variational integrators of fractional Lagrangian systems in the framework of discrete embeddings

Loïc Bourdin (1) , Jacky Cresson (2, 1) , Isabelle Greff (1) , Pierre Inizan (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a variational structure called Lagrangian structure. We are specially interested in the conservation at the discrete level of this Lagrangian structure by discrete embeddings. We then replace in this framework the variational integrators developed in [10, Chapter VI.6] and in [12]. Finally, we extend the notion of discrete embeddings and variational integrators to fractional Lagrangian systems.

Mots clés: Lagrangian systems; Variational integrator; Fractional calculus

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Loïc Bourdin, Jacky Cresson, Isabelle Greff, Pierre Inizan. Variational integrators of fractional Lagrangian systems in the framework of discrete embeddings. 11ème conférence internationale Saragosse-Pau sur les Mathématiques Appliquées, 2010, Jaca, Spain. ⟨hal-00868514⟩