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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Detalles Bibliográficos
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
Descripción
Sumario: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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