We present and compare different numerical schemes for the integration of the variational
equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the …

We present a comparison of different numerical techniques for the integration of variational
equations. The methods presented can be applied to any autonomous Hamiltonian system …

We discuss some of the contributions, made by the authors and their research group, on the
numerical methods for Hamiltonian systems. Our main concern will be the Hamiltonian …

Symplectic algorithms have been shown to be a right formalism for numerical computation of
Hamiltonian systems. They are suitable to long time computation and of good qualitative …

A method for constructing time-step-based symplectic maps for a generic Hamiltonian
system subjected to perturbation is developed. Using the Hamilton-Jacobi method and …

We study the problem of efficient integration of variational equations in multidimensional
Hamiltonian systems. For this purpose, we consider a Runge–Kutta-type integrator, a Taylor …

We modify the logarithmic Hamiltonian of Mikkola and Tanikawa by adding a constant (or
function) to both the kinetic energy and the force function. Explicit symplectic algorithms are …

Based on the method of canonical transformation of variables and the classical perturbation
theory, this innovative book treats the systematic theory of symplectic mappings for …

The present paper gives a brief survey of results from a systematic study, undertaken by the
authors and their colleagues, on the symplectic approach to the numerical computation of …

We present a survey of a recent comprehensive study on the numerical methods for
Hamiltonian systems based on symplectic geometry, together the motivations for the …