On the order reduction

In this work we present an extension of the technique order reduction to higher perturbative approximations in iterative fashion. The intention is also analyze more carefully conditions for validity technique. With mind, a few simple situations which converges analytically exact solutions are presented as examples. It discovered that does not converge weak coupling limit most known schemes, at least when applied these Also, considering specific examples, convergence occurs strong regimes. As realistic case, Starobinsky's inflationary model presented. verified method solution slow-roll regime.