  In the Renormalised Perturbation Theory (RPT) the Anderson impurity model is
interpreted in terms of renormalised parameters $\boldsymbol{\tilde{\mu}}=
(\tilde{\epsilon}_d, \tilde{\Delta}, \tilde{U})$ which are in a one-to-one
correspondence with the bare impurity level $\epsilon_d$, hybridisation
$\Delta$ and on-site interaction $U$. Though the renormalised parameters
suffice to describe the low-energy fixed point of the model, the parameters
themselves usually have to be determined using the Numerical Renormalisation
Group. In this paper we address this issue by applying the flow equation method
to the particle-hole symmetric model to derive a system of differential
equations for $ \textrm{d}\boldsymbol{\tilde{\mu}}/ \textrm{d} U$. To leading
order in $\tilde{U}$ this assumes a particularly simple form, permitting its
analytic solution in this approximation. We find that our results for the
renormalised parameters are in good agreement with the NRG and use them to
calculate the Wilson ratio, spin susceptibility and conductance of the
impurity.
