- Diego Navarro Pozo
Hamiltonian systems form one of the most important classes of differential equations describing the evolution of physical phenomena. They are the backbone of classical mechanics and their application covers many different areas such as molecular dynamics, hydrodynamics, celestial and statistical mechanics, just to mention a few of them. A noteworthy feature of Hamiltonian systems is that their flow possesses a geometric property -known as symplecticness- which have a major impact on the long-time behavior of the solution. Since in general closed-form solutions can be found only in few particular cases, the construction and analysis of numerical integrators -able to produce discrete approximations that are also symplecticity preserving- is crucial for studying these systems.
In this work we present the key ideas about Hamiltonian systems and their theoretical properties. We also review the main numerical methods and techniques to design and analyze symplectic integrators. Special attention is given to the stability and dynamical properties of the methods, as well as their effectiveness for long-term simulation. Finally, we propose an algorithm to improve the computational implementation of the family of exponential-based symplectic integrators recently proposed in the literature.
*Texto enviado pelo aluno.
Membros da banca:
- Hugo Alexander de la Cruz Cansino (orientador) – FGV/EMAp
- Maria Soledad Aronna - FGV/EMAp
- Moacyr Alvim Horta Barbosa da Silva – FGV/EMAp
- Daniel Gregório Alfaro Vigo - UFRJ