Numerical solution of Painlev̀e equation I by optimal homotopy asymptotic method Available to Purchase

The Painlev̀e equations are second order ordinary differential equations which can be grouped into six families, namely Painlev'e equation I, II, ..., VI. In this paper, we employed the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate solution of Painlev̀e equation I. The results obtained by OHAM are compared with those obtained by Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM), and excellent agreement has been found.