  We apply the renormalized perturbation theory (RPT) to the symmetric Anderson
impurity model. Within the RPT framework exact results for physical observables
such as the spin and charge susceptibility can be obtained in terms of the
renormalized values $\tilde{\boldsymbol\mu} = (\tilde{\Delta}, \tilde{U})$ of
the hybridization $\Delta$ and Coulomb interaction $U$ of the model. The main
difficulty in the RPT approach usually lies in the calculation of the
renormalized values themselves. In the present work we show how this can be
accomplished by deriving differential flow equations describing the evolution
of $\tilde{\boldsymbol \mu} (\Delta)$ with $\Delta$. By exploiting the fact
that $\tilde{\boldsymbol \mu} (\Delta)$ can be determined analytically in the
limit $\Delta \rightarrow \infty$ we solve the flow equations numerically to
obtain estimates for the renormalized parameters in the range
$0<U/\pi\Delta<3.5$.
