A note on the homotopy analysis method

Abstract

The present work is devoted to using an analytic approach, namely the homotopy analysis method, to obtain convergent series solutions of strongly nonlinear problems. On the basis of the homotopy derivative concept described in Liao (2009) [3], a theorem is proved here which generalizes some lemmas and theorems provided in Liao (2009) [3] and Molabahrami and Khani (2007) [4]. Significant applicability of the theorem obtained here in some practical situations is demonstrated. © 2010 Elsevier Ltd. All rights reserved.