On the polynomial solution of the first PainlevÃ© equation

20170322 https://doi.org/10.14419/ijamr.v6i1.6559 
PainlevÃ© transcendent, first PainlevÃ© equation, optimization methods. 
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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Sierra Porta, D., & NÃºÃ±ez, L. A. (2017). On the polynomial solution of the first PainlevÃ© equation. International Journal of Applied Mathematical Research, 6(1), 3438. https://doi.org/10.14419/ijamr.v6i1.6559