Extended homotopy perturbation method and computation of flow past a stretching sheet

We introduce an extended version of the homotopy perturbation method (HPM) for computing the steady flow of an incompressible, viscous fluid past a radially stretching sheet. In this version the independent variable is stretched by scaling it by a parameter that incorporates the homotopy parameter pp. The coefficients in the parameter are determined by requiring that the solutions obtained at each stage are free of secular terms. It is shown that the totally analytical solution developed by applying the extended version leads to a convergent sequence of homotopy solutions, the convergence of which can be accelerated by applying Shanks’ transformation.