Series Solution for Painlevé Equation II

Abstract

The Painlev'e equations are second order ordinary differential equations which can be grouped into six families, namely Painlev'e equation I, II,…, VI. This paper presents the series solution of second Painlevé equation via optimal homotopy asymptotic method (OHAM). This approach is highly efficient and it controls the convergence of the approximate solution. Comparison of the obtained solution via OHAM is provided with those obtained by Homotopy Perturbation Method (HPM), Adomian Decomposition Method (ADM), Sinc-collocation and Runge-Kutta 4 methods. It is revealed that there is an excellent agreement between OHAM and other published data which confirm the effectiveness of the OHAM. doi:10.14456/WJST.2015.43

Keywords

• Optimal homotopy asymptotic method
• Painlevé equation
• Nonlinear ODE