  Dynamic systems have a fundamental relevance in the description of physical
phenomena. The search for more accurate and faster numerical integration
methods for the resolution of such systems is, therefore, an important topic of
research. The present work introduces a new approach for the numerical
integration of dynamic systems. We propose an association of numerical
integration methods (integrators) in order to optimize the performance. The
standard we apply is the balance of the duo : precision obtained x running
time. The numerical integration methods we have chosen, for this particular
instance of association, were the Runge-Kutta of fourth order and seventheighth
order. The algorithm was implemented in C++ language. The results showed an
improvement in accuracy over the lower grade numerical integrator (actually, we
have achieved, basically, the precision of the top integrator) with a
processing time performance closer to the one of the lower grade integrator.
Similar results can be obtained for other pairs of numerical integration
methods.
