  I introduce an approximation scheme that allows to deduce differential
equations for the renormalization group $\beta$-function from a
Schwinger--Dyson equation for the propagator. This approximation is proven to
give the dominant asymptotic behavior of the perturbative solution. In the
supersymmetric Wess--Zumino model and a $\phi^3_6$ scalar model which do not
have divergent vertex functions, this simple Schwinger--Dyson equation for the
propagator captures the main quantum corrections.
