Shooting and parallel shooting methods for solving the Falkner-Skan boundary-layer equation

Abstract

We present three accurate and efficient numerical schemes for solving the Falkner-Skan equation with positive or negative wall shear. Newton's method is employed, with the aid of the variational equations, in all the schemes and yields quadratic convergence. First, ordinary shooting is used to solve for the case of positive wall shear. Then a nonlinear eigenvalue technique is introduced to solve the inverse problem in which the wall shear is prescribed and the pressure distribution is to be determined. With this approach the reverse flow solutions (i.e., negative wall shear) are obtained. Finally, a parallel shooting method is employed to reduce the sensitivity of the convergence of the iterations to the initial estimates.

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