Approximations of the nonlinear Painlevé transcendents

In this communication, we apply the new homotopy perturbation method (NHPM) to solve the first and second Painlevé transcendent. The NHPM for solving differential equations based on two component procedure and polynomial initial condition. The numerical results are compared with existing analytic results obtained by Adomian decomposition method (ADM), homotopy perturbation method (HPM), analytic continuation method and Legendre Tau method. The outcomes confirm that the scheme yields accurate and excellent results even when two components are used.