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
generalized momenta and whose potential is a function of the generalized positions. We
apply these techniques to Hamiltonian systems of various degrees of freedom and
investigate their efficiency in accurately reproducing well-known properties of chaos
indicators such as the Lyapunov characteristic exponents and the generalized alignment …

Introduction. In solving a system of algebraic equations it is well known that the problem is
much simpler if the equations are linear. In solving a system of differential equations, one
usually does not really care if the equations are linear or not, even though a simplification is
possible in the linear case; namely by observing that in a predictor-corrector method the
corrector can be solved explicitly for the unknown without predicting. This simplification
effectively iterates the corrector to convergence with just a single computation, giving better …