A new comparative study between homotopy analysis transform method and homotopy perturbation transform method on a semi infinite domain

The aim of this article is to introduce a new approximate method, namely homotopy analysis transform method (HATM) which is a combination of homotopy analysis method (HAM) and Laplace decomposition method (LDM) to provide an analytical approximate solution to Blasius flow equations. The proposed scheme finds the solutions of nonlinear problems without any discretization, restrictive assumptions and avoids the rounding-off errors. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method (HPTM). A good agreement between the obtained solution and some well-known results has been demonstrated.