On the application of homotopy perturbation method to differential equations

We show that a recent application of homotopy perturbation method to a class of ordinary differential equations yields either useless or wrong results. There has recently been great interest in the application of several approximate procedures, like the homotopy perturbation method (HPM), the Adomian decomposition method (ADM), and the variation iteration method (VIM), to a variety of linear and nonlinear problems of interest in theoretical physics [1–15]. For brevity I will call VAPA all those variational and perturbational approaches. In a series of papers I have shown that most of the results produced by those methods are useless, nonsensical, and worthless [16–19]. However, my criticisms have not been welcome and for that reason they remain unpublished outside arXiv. In a recent paper Rafiq et al [13] applied the HPM to some ordinary second– order differential equations, and the purpose of this comment is to discuss their results. 1 e–mail: [email protected] Preprint submitted to Elsevier 9 September 2008 Rafiq et al [13] solved second order differential equations of the form