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 o...

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Autores principales: Vazquez-Leal, Hector, Benhammouda, Brahim, Filobello-Nino, Uriel Antonio, Sarmiento-Reyes, Arturo, Jimenez-Fernandez, Victor Manuel, Marin-Hernandez, Antonio, Herrera-May, Agustin Leobardo, Diaz-Sanchez, Alejandro, Huerta-Chua, Jesus
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2014
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4000591/
https://www.ncbi.nlm.nih.gov/pubmed/24790815
http://dx.doi.org/10.1186/2193-1801-3-160
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author Vazquez-Leal, Hector
Benhammouda, Brahim
Filobello-Nino, Uriel Antonio
Sarmiento-Reyes, Arturo
Jimenez-Fernandez, Victor Manuel
Marin-Hernandez, Antonio
Herrera-May, Agustin Leobardo
Diaz-Sanchez, Alejandro
Huerta-Chua, Jesus
author_facet Vazquez-Leal, Hector
Benhammouda, Brahim
Filobello-Nino, Uriel Antonio
Sarmiento-Reyes, Arturo
Jimenez-Fernandez, Victor Manuel
Marin-Hernandez, Antonio
Herrera-May, Agustin Leobardo
Diaz-Sanchez, Alejandro
Huerta-Chua, Jesus
author_sort Vazquez-Leal, Hector
collection PubMed
description 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. AMS SUBJECT CLASSIFICATION: 34L30
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spelling pubmed-40005912014-04-30 Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals Vazquez-Leal, Hector Benhammouda, Brahim Filobello-Nino, Uriel Antonio Sarmiento-Reyes, Arturo Jimenez-Fernandez, Victor Manuel Marin-Hernandez, Antonio Herrera-May, Agustin Leobardo Diaz-Sanchez, Alejandro Huerta-Chua, Jesus Springerplus Research 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. AMS SUBJECT CLASSIFICATION: 34L30 Springer International Publishing 2014-03-25 /pmc/articles/PMC4000591/ /pubmed/24790815 http://dx.doi.org/10.1186/2193-1801-3-160 Text en © Vazquez-Leal et al.; licensee Springer. 2014 This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research
Vazquez-Leal, Hector
Benhammouda, Brahim
Filobello-Nino, Uriel Antonio
Sarmiento-Reyes, Arturo
Jimenez-Fernandez, Victor Manuel
Marin-Hernandez, Antonio
Herrera-May, Agustin Leobardo
Diaz-Sanchez, Alejandro
Huerta-Chua, Jesus
Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals
title Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals
title_full Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals
title_fullStr Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals
title_full_unstemmed Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals
title_short Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals
title_sort modified taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4000591/
https://www.ncbi.nlm.nih.gov/pubmed/24790815
http://dx.doi.org/10.1186/2193-1801-3-160
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