  Extensive N-body simulations are among the key means for the study of
numerous astrophysical and cosmological phenomena, so various schemes are
developed for possibly higher accuracy computations. We demonstrate the
principal possibility for revealing the evolution of a perturbed Hamiltonian
system with an accuracy independent on time. The method is based on the Laplace
transform and the derivation and analytical solution of an evolution equation
in the phase space for the resolvent and using computer algebra.
