In this study, New Variational Homotopy Pez’turbation Method (NVHPM) was employed to approximate solutions of Painlevé Equation I, with its initial conditions. NVHPM based on coupling of VIM and HPM as introduced by Hesameddini and Latifizadeh.[1}, with some good modification was engaged for the purpose of this study. In this paper we apply the NVHPM to Painlevé Equation I as given by Hesameddini and Peyrovi to find its approximate solutions. The advantage of the new Scheme is that it does not require discritization, linearization or any restrictive assumption of any form before it is applied. Numerical comparisons are made between VIM/HPM and NVHPM results.
Keywords: Painlevé Equations, Variational Iteration Method, Homotopy Perturbation Method, New Variational Homotopy Perturbation Method, Ordinary Differential Equations
Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 619 – 622