Comments on ``Homotopy perturbation method for solving reaction-diffusion equations'' (Q1955045)

The author argues that, in an article by \textit{Y. X. Wang} et al. [Math. Probl. Eng. 2008, Article ID 795838 (2008; Zbl 1173.35551)], the homotopy perturbation method was applied to a one-dimensional boundary value problem in such a way that errors grow indefinitely as more terms of the approximation are taken into account. He proposes another choice of the initial approximation and of the initial conditions for the higher-order terms which lead to better results for the problems \(u''+u^2=0\) and \(u''+u^3=0\) with Dirichlet boundary conditions.