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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 923975, 21 pages
http://dx.doi.org/10.1155/2012/923975
Research Article

Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version

1Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Cto. Gonzalo Aguirre Beltrán s/n, 91000 Xalapa, VER, Mexico
2Department of Electronics, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1, 72840 Santa María Tonantzintla, PUE, Mexico
3Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received 25 September 2012; Accepted 21 October 2012

Academic Editor: Chein-Shan Liu

Copyright © 2012 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.

Citations to this Article [19 citations]

The following is the list of published articles that have cited the current article.

  • Hector Vazquez-Leal, “Exploring a piece-wise-nonlinear method,” Computational and Applied Mathematics, 2013. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, “Generalized homotopy method for solving nonlinear differential equations,” Computational and Applied Mathematics, 2013. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, “Piece-wise-polynomial method,” Computational and Applied Mathematics, 2013. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, and Francisco Guerrero, “Application of series method with Padé and Laplace-Padé resummation methods to solve a model for the evolution of smoking habit in Spain,” Computational and Applied Mathematics, 2013. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, Yasir Khan, Uriel Filobello-Nino, Arturo Sarmiento-Reyes, Alejandro Diaz-Sanchez, and Luis-F. Cisneros-Sinencio, “Fixed-Term Homotopy,” Journal of Applied Mathematics, vol. 2013, pp. 1–11, 2013. View at Publisher · View at Google Scholar
  • H. Vazquez-Leal, K. Boubaker, L. Hernandez-Martinez, and J. Huerta-Chua, “Approximation for Transient of Nonlinear Circuits Using RHPM and BPES Methods,” Journal of Electrical and Computer Engineering, vol. 2013, pp. 1–6, 2013. View at Publisher · View at Google Scholar
  • Vazquez-Leal, Khan, Sarmiento-Reyes, Filobello-Nino, Diaz-Sanchez, Jimenez-Fernandez, Herrera-May, Cervantes-Perez, and Huerta-Chua, “Homotopy-continuation picard method,” Applied Mathematical Sciences, vol. 7, no. 129-132, pp. 6429–6439, 2013. View at Publisher · View at Google Scholar
  • Vazquez-Leal, Castaneda-Sheissa, Sarmiento-Reyes, Khan, Hernandez-Martinez, Sanchez-Orea, Herrera-May, Jimenez-Fernandez, Diaz-Sanchez, and Huerta-Chua, “Symbolic analysis and reordering of nonlinear circuit's equations in order to accelerate homotopy simulation,” Applied Mathematical Sciences, vol. 7, no. 129-132, pp. 6441–6464, 2013. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, Brahim Benhammouda, Uriel Filobello-Nino, Arturo Sarmiento-Reyes, Victor Manuel Jimenez-Fernandez, Jose Luis Garcia-Gervacio, Jesus Huerta-Chua, Luis Javier Morales-Mendoza, and Mario Gonzalez-Lee, “Direct application of Padé approximant for solving nonlinear differential equations,” Journal of the Korean Physical Society, vol. 3, no. 1, pp. 1–11, 2014. View at Publisher · View at Google Scholar
  • Uriel Filobello-Nino, Alejandro Diaz-Sanchez, Jesus Huerta-Chua, Juan Cervantes-Perez, Hector Vazquez-Leal, Brahim Benhammouda, Luis Hernandez-Martinez, Claudio Hoyos-Reyes, Jose Antonio Agustin Perez-Sesma, Victor Manuel Jimenez-Fernandez, Domitilo Pereyra-Diaz, and Antonio Marin-Hernandez, “Nonlinearities distribution Laplace transform-homotopy perturbation method,” Journal of the Korean Physical Society, vol. 3, no. 1, pp. 1–13, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Suares Clovis Noutchie Oukouomi, “Novel Approach for Dealing with Partial Differential Equations with Mixed Derivatives,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, Brahim Benhammouda, Uriel Antonio Filobello-Nino, Arturo Sarmiento-Reyes, Victor Manuel Jimenez-Fernandez, Antonio Marin-Hernandez, Agustin Leobardo Herrera-May, Alejandro Diaz-Sanchez, and Jesus Huerta-Chua, “Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals,” SpringerPlus, vol. 3, no. 1, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, and Arturo Sarmiento-Reyes, “GHM method for obtaining rational solutions of nonlinear differential equations,” SpringerPlus, vol. 4, no. 1, 2015. View at Publisher · View at Google Scholar
  • U. Filobello-Nino, H. Vazquez-Leal, Yasir Khan, M. Sandoval-Hernandez, A. Perez-Sesma, A. Sarmiento-Reyes, Brahim Benhammouda, V. M. Jimenez-Fernandez, J. Huerta-Chua, S. F. Hernandez-Machuca, J. M. Mendez-Perez, L. J. Morales-Mendoza, and M. Gonzalez-Lee, “Extension of Laplace transform–homotopy perturbation method to solve nonlinear differential equations with variable coefficients defined with Robin boundary conditions,” Neural Computing and Applications, 2015. View at Publisher · View at Google Scholar
  • Brahim Benhammouda, “Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method,” SpringerPlus, vol. 4, no. 1, 2015. View at Publisher · View at Google Scholar
  • Brahim Benhammouda, and Hector Vazquez-Leal, “Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism,” Discrete Dynamics in Nature and Society, vol. 2015, pp. 1–14, 2015. View at Publisher · View at Google Scholar
  • Ismail M. Abdelrazik, Hesham A. Elkaranshawy, and Amr M. Abdelrazek, “Modified Parker-Sochacki method for solving nonlinear oscillators,” Mechanics Based Design of Structures and Machines, pp. 1–14, 2016. View at Publisher · View at Google Scholar
  • Hector Vazquez-Leal, Hüseyin Koçak, and Inan Ates, “Rational Approximations for Heat Radiation and Troesch's Equations,” International Journal of Computational Methods, vol. 13, no. 3, 2016. View at Publisher · View at Google Scholar
  • U. Filobello-Nino, H. Vazquez-Leal, M. M. Rashidi, H. M. Sedighi, A. Perez-Sesma, M. Sandoval-Hernandez, A. Sarmiento-Reyes, A. D. Contreras-Hernandez, D. Pereyra-Diaz, C. Hoyos-Reyes, V. M. Jimenez-Fernandez, J. Huerta-Chua, F. Castro-Gonzalez, and J. R. Laguna-Camacho, “Laplace transform homotopy perturbation method for the approximation of variational problems,” SpringerPlus, vol. 5, no. 1, 2016. View at Publisher · View at Google Scholar