title: Direct application of Padé approximant for solving nonlinear differential equations.
abstract: This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant.
  
  
  METHODS
  34L30.
authors.affiliation: Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Mexico.
authors.forename: Hector
authors.initials: H
authors.lastname: Vazquez-Leal
authors.affiliation: Higher Colleges of Technology, Abu Dhabi Men's College, P.O. Box 25035, Abu Dhabi, United Arab Emirates.
authors.forename: Brahim
authors.initials: B
authors.lastname: Benhammouda
authors.affiliation: Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Mexico.
authors.forename: Uriel
authors.initials: U
authors.lastname: Filobello-Nino
authors.affiliation: National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro No. 1, Sta. Maria, 72840 Tonantzintla, Puebla México.
authors.forename: Arturo
authors.initials: A
authors.lastname: Sarmiento-Reyes
authors.affiliation: Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Mexico.
authors.forename: Victor Manuel
authors.initials: VM
authors.lastname: Jimenez-Fernandez
authors.affiliation: Dirección General de la Unidad de Estudios de Posgrado, Universidad Veracruzana, Av. Paseo de las Palmas No. 15 esq. Los Mangos, Fracc. Jardines de las Ánimas, 91000 Xalapa, Veracruz México.
authors.forename: Jose Luis
authors.initials: JL
authors.lastname: Garcia-Gervacio
authors.affiliation: Facultad de Ingenieria Civil, Universidad Veracruzana, Venustiano Carranza S/N, Col. Revolucion, 93390 Poza Rica, Veracruz México.
authors.forename: Jesus
authors.initials: J
authors.lastname: Huerta-Chua
authors.affiliation: Department of Electronics Engineering, Universidad Veracruzana, Venustiano Carranza S/N, Col. Revolucion, 93390 Poza Rica, Veracruz México.
authors.forename: Luis Javier
authors.initials: LJ
authors.lastname: Morales-Mendoza
authors.affiliation: Department of Electronics Engineering, Universidad Veracruzana, Venustiano Carranza S/N, Col. Revolucion, 93390 Poza Rica, Veracruz México.
authors.forename: Mario
authors.initials: M
authors.lastname: Gonzalez-Lee
keywords: Nonlinear differential equations; Padé transform