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Mathematical Problems in Engineering
Volume 2015, Article ID 717404, 7 pages
http://dx.doi.org/10.1155/2015/717404
Research Article

Power Series Extender Method for the Solution of Nonlinear Differential Equations

1Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán, S/N, 91000 Xalapa, VER, Mexico
2National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro No. 1, Santa Maria, 72840 Tonantzintla, PUE, Mexico

Received 1 October 2014; Accepted 1 December 2014

Academic Editor: Salvatore Alfonzetti

Copyright © 2015 Hector Vazquez-Leal and Arturo Sarmiento-Reyes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a power series extender method to obtain approximate solutions of nonlinear differential equations. In order to assess the benefits of this proposal, three nonlinear problems of different kind are solved and compared against the power series solution obtained using an approximative method. The problems are homogeneous Lane-Emden equation of index, governing equation of a burning iron particle, and an explicit differential-algebraic equation related to battery model simulations. The results show that PSEM generates highly accurate handy approximations requiring only a few steps. The main advantage of PSEM is to extend the domain of convergence of the power series solutions of approximative methods as Taylor series method, homotopy perturbation method, homotopy analysis method, variational iteration method, differential transform method, and Adomian decomposition method, among many others. From the application of PSEM, it results in handy easy computable expressions that extend the domain of convergence of high order power series solutions.