Approximation of Hamiltonian Systems using an Alternative Variational Technique

Authors

Sergio Amat, Departamento de Matem´atica Aplicada y Estad´ıstica, Universidad Polit´ecnica de Cartagena, SpainFollow
M. José Legaz, Departamento de Matem´atica Aplicada y Estad´ıstica, Universidad Polit´ecnica de Cartagena, SpainFollow
Pablo Pedregal, E.T.S. Ingenieros Industriales, Universidad de Castilla La Mancha, Campus de Ciudad Real SpainFollow

Author Country (or Countries)

Spain

Abstract

Hamiltonian systems are related to numerous areas of mathematics and have a lot of application branches, such as classical and quantum mechanics, statistics, optical, astronomy, molecular dynamic, plasma physics, etc. In general, the integration of these systems requires the use of geometric integrators. In this paper, we introduce a new variational approach for models which are formulated naturally as conservative systems of ODEs, most importantly Hamiltonian systems. Our variational method for Hamiltonian systems, which is proposed here, is in some sense symplectic and energy preserving. In addition to introducing the technique, we briefly indicate its most basic properties, and test its numerical performance in some simple examples

Recommended Citation

Amat, Sergio; José Legaz, M.; and Pedregal, Pablo (2023) "Approximation of Hamiltonian Systems using an Alternative Variational Technique," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 21.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/21