  In this paper, we review the so-called T\"opfer algorithm that allows us to
find a non-iterative numerical solution of the Blasius problem, by solving a
related initial value problem and applying a scaling transformation. Moreover,
we remark that the applicability of this algorithm can be extended to any given
problem, provided that the governing equation and the initial conditions are
invariant under a scaling group of point transformations and that the
asymptotic boundary condition is non-homogeneous. Then, we describe an
iterative extension of T\"opfer's algorithm that can be applied to a general
class of problems. Finally, we solve the Falkner-Skan model, for values of the
parameter where multiple solutions are admitted, and report original numerical
results, in particular data related to the famous reverse flow solutions by
Stewartson. The numerical data obtained by the extended algorithm are in good
agreement with those obtained in previous studies.
