Variable step size does not harm second-order integrators for Hamiltonian systems
The author describes a number of experiments that have been performed with symplectic integrators for the two-body problem. It is shown that the variable stepsize symplectic integrators do not in general give rise to quadratic growth of the error, i.e. the variable stepsize does not degrade the performance of second-order symplectic integrators. The same refers to variable stepsize nonsymplectic methods. This conclusion is opposed to a report of \textit{M. P. Calvo} and \textit{J. M. Sanz-Serna} [Report 1991/3, Appl. Math. Comput., Univ. Valladolid (1991)] in which the authors indicate that for explicit symplectic integrator applied to the two-body problem, fixed stepsize gives a linear growth of the error, while nonsymplectic and variable stepsize symplectic integrators force the error to grow quadratically.
scientific article; zbMATH DE number 428541