Numerical Spline Algorithm for Solving Falkner–Skan Equation (Latakia University Journal -Basic Sciences Series, 2019)
This paper presents a numerical spline algorithm for the Falkner–Skan equation (FSE) over a semi-infinite interval. This algorithm is based on change of variable from interval  to [0,1], then the FSE is transformed into first initial value problem (IVP) and second IVP for improving convergence.  Spline polynomials with four collocation points are applied directly to the IVPs without their reducing to a system of first-order differential equations. The study shows that purposed algorithm is consistent and convergent with a global truncation error from order eighth. The efficacy of our algorithm is tested by solving the problems of Blasius, Pohlhausen, Homann and Hiemenz flows, and other special cases over various intervals, where the results of comparisons with other methods indicate the efficiency of our algorithm and enable it to provide solutions with high numerical accuracy.