# On the polynomial solution of the first PainlevÃ© equation

## DOI:

https://doi.org/10.14419/ijamr.v6i1.6559## Published:

2017-03-22## Keywords:

PainlevÃ© transcendent, first PainlevÃ© equation, optimization methods.## Abstract

The PainlevÃ© equations and their solutions arises in pure, applied mathematics and theoretical physics. In this manuscript we apply the Optimal Homotopy Asymptotic Method (OHAM) for solving the first PainlevÃ© equation. Our approximation technique is based on the use of polynomial solutions, which are shown to be accurate when compared to the computed numerical solutions, thus providing a very close description of the evolution of the system.

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