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

2016/01/19 by Loïc Bourdin, Bourdin, Loïc, Jacky Cresson +5
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1601.04882

openalex publication_date 2016/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Mid-point embedding of Hamiltonian systems and variational integrators
• On the exact discrete Lagrangian function for variational integrators: theory and applications
• Discrete embeddings for Lagrangian and Hamiltonian systems
• Fractional damping through restricted calculus of variations
• General Techniques for Constructing Variational Integrators