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Journal of Applied Mathematics
Volume 2013, Article ID 972704, 11 pages
Research Article

Fixed-Term Homotopy

1Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Circuito Gonzalo Aguirre Beltrán s/n, 91000 Xalapa, VER, Mexico
2Department of Mathematics, Zhejiang University, Hangzhou 310027, China
3Department of Electronics, National Institute for Astrophysics, Optics, and Electronics, Luis Enrique Erro No. 1, 72840 Sta. María Tonantzintla, PUE, Mexico

Received 6 September 2012; Revised 6 December 2012; Accepted 20 December 2012

Academic Editor: Chein-Shan Liu

Copyright © 2013 Hector Vazquez-Leal et al. 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.


A new tool for the solution of nonlinear differential equations is presented. The Fixed-Term Homotopy (FTH) delivers a high precision representation of the nonlinear differential equation using only a few linear algebraic terms. In addition to this tool, a procedure based on Laplace-Padé to deal with the truncate power series resulting from the FTH method is also proposed. In order to assess the benefits of this proposal, two nonlinear problems are solved and compared against other semianalytic methods. The obtained results show that FTH is a power tool capable of generating highly accurate solutions compared with other methods of literature.