Fer's factorization as a symplectic integrator
The author presents the Fer expansion as a possible explicit symplectic integrator for time-dependent Hamiltonian systems. When this iterative procedure is applied to an arbitrary Hamiltonian, a factorization of the time-evolution map is obtained as an infinite product of Lie transformations. The author shows that, at least for quadratic Hamiltonians, very few iterations are sufficient to achieve accurate results both for the orbits and conserved quantities. Numerical experiments presented in this paper show the performance of the proposed method. The third- and fourth-order Fer expansions are compared with other numerical integration schemes, including symplectic ones. It appears that the performance of the Fer factorization is comparable to that of the Gragg-Bulirsch-Stoer extrapolation algorithm, and it is better than other symplectic integration methods such as the explicit Runge-Kutta-Nyström and Gauss-Legendre Runge-Kutta algorithms.
Gragg-Bulirsch-Stoer extrapolation algorithm
scientific article; zbMATH DE number 932030