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

Abstract

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.

11ème conférence internationale Saragosse-Pau sur les Mathématiques Appliquées, 2010, Jaca, Spain. 2010. arXiv admin note: substantial text overlap with arXiv:1103.0465

References in corpus (1)

• Discrete-Time Fractional Variational Problems

Cited by in corpus (2)

• Generalized fractional calculus with applications to the calculus of variations
• Differential, integral, and variational delta-embeddings of Lagrangian systems