Approximate analytical solution of nonlinear third-order singularly perturbed BVPs using homotopy analysis method-padé method

In this paper we propose a reliable algorithm to develop approximate analytical solutions of a class of nonlinear third order singularly perturbed boundary-value problems exhibiting boundary layers. In this method, the given problem is transformed into a nonlinear system of two ODEs, with suitable initial and boundary conditions and a zero-order asymptotic solution of the transformed system is constructed. Then, the reduced initial value system is solved using a combination of homotopy analysis method and Padé approximant (HAM-P). The convergence and error analysis of the method is presented. A comparison between the solutions obtained by HAM and HAM-P with exact solutions is presented and revealed that the proposed method is very effective and convenient for solving such type of nonlinear boundary-value problems with boundary layers.