Spectral-Homotopy analysis method for solving a nonlinear second order BVP

Abstract

A modification of the homotopy analysis method(HAM)for solving nonlinear second order boundary value problem(BVP) is proposed.the implementation of new approach is demonstrate by solving the Darcy-Brinkman-Forchheimer equation for steady fully developed fluid flow in a horizontal channel filled with a prous medium.The model equation is solved concurrently using the standard HAM approach and numerically using a shooting method based on the fourth order Rang-Kutta scheme.The results demonstrate that the new spectral homotopy analysis method is more efficient and converges faster than the standard homotopy analysis method