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In this paper, we review the so-called T\"opfer algorithm that allows us tofind a non-iterative numerical solution of the Blasius problem, by solving arelated initial value problem and applying a scaling transformation. Moreover,we remark that the applicability of this algorithm can be extended to any givenproblem, provided that the governing equation and the initial conditions areinvariant under a scaling group of point transformations and that theasymptotic boundary condition is non-homogeneous. Then, we describe aniterative extension of T\"opfer's algorithm that can be applied to a generalclass of problems. Finally, we solve the Falkner-Skan model, for values of theparameter where multiple solutions are admitted, and report original numericalresults, in particular data related to the famous reverse flow solutions byStewartson. The numerical data obtained by the extended algorithm are in goodagreement with those obtained in previous studies.

Blasius Problem and Falkner-Skan model: T\"opfer's Algorithm and its Extension