Numerical Solution of Painlevé Equation II via Daftardar–Gejji and Jafari Method

Abstract

Painleve II equation is one of the six second-order ordinary differential equations namely Painleve equations. This paper presented the numerical solution for Painleve equation II via a new iterative method called Daftardar–Gejji and Jafari method (DJM). Comparison of the results obtained by DJM with those obtained by other methods such as optimal homotopy asymptotic method (OHAM), homotopy perturbation method (HPM), Sinc-collocation method, Chebyshev series method (CSM) and variational iterative method (VIM), revealed the effectiveness of the method.