  The renormalization group equations of massive $\mathcal{N}=1$ supersymmetric
quantum electrodynamics (SQED) are studied using the functional renormalization
group approach. A non-perturbative form of the beta function has been computed
via a derivative expansion of the effective action. In the local potential
approximation, the functional form of the non-perturbative beta function is
closely related to the form of the NSVZ exact beta function; this relationship
is exact if an effective fine-structure constant is defined. The non-massive
limit of the same is also analyzed. Furthermore, the calculation of the beta
function has been improved by incorporating the influence of momentum modes on
the propagation of the superfields in the non-perturbative running of the
electric charge, applying a second-order truncation for the derivative
expansion, which we use to find the momentum contributions to the $\beta$
function. Again, we find the NSVZ relation for an effective fine-structure
constant.
