title: Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.
abstract: In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations.
  
  
  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 Antonio
authors.initials: UA
authors.lastname: Filobello-Nino
authors.affiliation: National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro No. 1, Sta. Maria, 72840 Tonantzintla, Puebla Mexico.
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: Department of Artificial Intelligence, Universidad Veracruzana, Sebastián Camacho 5 Centro, 91000 Xalapa, Veracruz Mexico.
authors.forename: Antonio
authors.initials: A
authors.lastname: Marin-Hernandez
authors.affiliation: Micro and Nanotechnology Research Center, Universidad Veracruzana, Calzada Ruiz Cortines 455, Boca del Rio, 94292 Veracruz Mexico.
authors.forename: Agustin Leobardo
authors.initials: AL
authors.lastname: Herrera-May
authors.affiliation: National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro No. 1, Sta. Maria, 72840 Tonantzintla, Puebla Mexico.
authors.forename: Alejandro
authors.initials: A
authors.lastname: Diaz-Sanchez
authors.affiliation: Facultad de Ingenieria Civil, Universidad Veracruzana, Venustiano Carranza S/N, Col. Revolucion, 93390 Poza Rica, Veracruz Mexico.
authors.forename: Jesus
authors.initials: J
authors.lastname: Huerta-Chua
keywords: Boundary valued problems; Dirichlet conditions; Mixed boundary conditions; Shooting technique; Taylor series method