A second-order finite-difference method for the Falkner-Skan equation

The Falkner-Skan equation arises in the study of laminar boundary layers exhibiting similarity. Numerical methods reported in the literature thus far are based on shooting methods and finite-difference methods obtained by first truncating the semi-infinite physical domain of the problem to a finite domain at an unknown finite boundary, which is determined as part of the solution by imposing an ''asymptotic boundary condition'' at this boundary. The method presented in this paper transforms the semi-infinite domain without truncating it to a finite domain and without imposing the asymptotic condition. This is accomplished by a coordinate transformation which maps the physical domain [0,~) directly to the computational domain [0,1]. The effectiveness of the method is illustrated by applying it successfully to various instances of the Falkner-Skan equation, and by demonstrating second-order accuracy.