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Mathematical Problems in Engineering
Volume 2012, Article ID 309123, 19 pages
http://dx.doi.org/10.1155/2012/309123
Research Article

Modified HPMs Inspired by Homotopy Continuation Methods

1Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Circuito Gonzalo Aguirre Beltrán s/n, 91000 Xalapa, VER, Mexico
2Department of Electronics, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1, 72840 Sta. María Tonantzintla, PUE, Mexico

Received 8 November 2011; Revised 15 December 2011; Accepted 18 December 2011

Academic Editor: Anuar Ishak

Copyright © 2012 Héctor Vázquez-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.

Abstract

Nonlinear differential equations have applications in the modelling area for a broad variety of phenomena and physical processes; having applications for all areas in science and engineering. At the present time, the homotopy perturbation method (HPM) is amply used to solve in an approximate or exact manner such nonlinear differential equations. This method has found wide acceptance for its versatility and ease of use. The origin of the HPM is found in the coupling of homotopy methods with perturbation methods. Homotopy methods are a well established research area with applications, in particular, an applied branch of such methods are the homotopy continuation methods, which are employed on the numerical solution of nonlinear algebraic equation systems. Therefore, this paper presents two modified versions of standard HPM method inspired in homotopy continuation methods. Both modified HPMs deal with nonlinearities distribution of the nonlinear differential equation. Besides, we will use a calcium-induced calcium released mechanism model as study case to test the proposed techniques. Finally, results will be discussed and possible research lines will be proposed using this work as a starting point.