**Abstract: **
Some practical consequences on the molecular-dynamics simulations
arising from a recently published numerical algorithm are
presented. The algorithm is not a finite-difference method and
therefore it could represent a complementary approach to the
traditional numerical integration of the equations of motion. It
consists of two steps. First, an analytic form of polynomials in
some formal parameter lambda (set to one in the following) is
derived, which approximate the solution of the system of
differential equations under consideration. Next, the numerical
values of the derived polynomials in the interval, in which the
difference between them and their truncated part of smaller degree
does not exceed a given accuracy epsilon, become the numerical
solution. The particular examples, which we have considered,
represent the forced linear and nonlinear oscillator and the 2D
Lennard-Jones fluid. In the latter case we have restricted our
attention to the polynomials of the first degree in the formal
parameter lambda.