Approximate differential equations for renormalization group functions in models free of vertex divergencies

I introduce an approximation scheme that allows to deduce differential equations for the renormalization group β-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 ϕ63 scalar model which do not have divergent vertex functions, this simple Schwinger-Dyson equation for the propagator captures the main quantum corrections.