Total Variation in Hamiltonian Formalism and Symplectic-Energy integrators

Abstract

We present a discrete total variation calculus in Hamiltonian formalism in this paper. Using this discrete variation calculus and generating functions for the flows of Hamiltonian systems, we derive two-step symplectic-energy integrators of any finite order for Hamiltonian systems from a variational perspective. The relationship between symplectic integrators derived directly from the Hamiltonian systems and the variationally derived symplectic-energy integrators is explored.

14 pages, 0 figures

References in corpus (3)

• Difference Discrete Variational Principle,EULER-Lagrange Cohomology and Symplectic, Multisymplectic Structures
• Total Variation and Variational Symplectic-Energy-Momentum integrators
• A Note on Symplectic Algorithms

Cited by in corpus (6)

• Variations in Discrete Mechanics and Field Theory
• Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
• How to regularize a symplectic-energy-momentum integrator
• Is Symplectic-Energy-Momentum Integration Well-Posed?
• On the Polysymplectic Integrator for the Short Pulse Equation
• An adaptive symplectic integrator for gravitational dynamics