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

Numerical Transformation Methods for a Moving-Wall Boundary Layer Flow of a Rarefied Gas Free Stream over a Moving Flat Plate