Some algebraic approach for the second Painlevé equation using the optimal homotopy asymptotic method (OHAM)

The study of Painlevé's equations has increased during the last years, due to the awareness that these equations and their solutions can accomplish good results both in the field of pure mathematics and theoretical physics. In this paper we introduced an optimal homotopy asymptotic method (OHAM) approach to propose analytic approximate solutions to the second Painlevé equation. The advantage of this method is that it provides a simple algebraic expression that can be used for further developments while maintaining good performance and fitting closely the numerical solution.