  The first contribution of this paper is the extension of the non-iterative
transformation method, proposed by T\"opfer more than a century ago and defined
for the numerical solution of the Blasius problem, to a Blasius problem with
extended boundary conditions. This method, which makes use of the invariance of
two physical parameters with respect to a scaling group of point
transformation, allows us to solve numerically the Blasius problem with
extended boundary conditions by solving a related initial value problem and
then rescaling the obtained numerical solution. Therefore, our method is an
initial value method. However, in this way, we cannot fix in advance the
physical parameters, and if we need just to compute the numerical solution for
given values of the two parameters we have to define an iterative extension of
the transformation method, which is the second contribution of this work.

Numerical Analysis;Numerical Analysis