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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.23 n.1 San José Jan./Jun. 2016
Artículos
Solución analítica de la ecuación diferencial ordinaria autónoma de orden k
Analytical solution of the k-th order autonomous ordinary differential equation
1Departamento de Matemática, Universidad del Atlántico, Barranquilla, Colombia. E-Mail: rjol1805@hotmail.com
El objetivo principal de este trabajo es hallar la solución analítica de la ecuación autónoma y ( k ) = f (y) y demostrar su convergencia usando polinomios autónomos de orden k, definidos aquí, además de la fórmula de Faá di Bruno para composición de funciones y polinomios de Bell. Los polinomios autónomos de orden k están definidos en término de los valores de frontera de la ecuación. Además valores especiales de los polinomios autónomos de orden 1 son dados.
Palabras clave: ecuación autónoma; polinomios de Bell; polinomios autónomos
The main objective of this paper is to find the analytical solution of the autonomous equation y ( k ) = f (y) and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.
Keywords: Autonomous equation; Bell polynomials; Autonomous polynomials
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Recibido: 09 de Septiembre de 2013; Revisado: 22 de Agosto de 2015; Aprobado: 22 de Septiembre de 2015
Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons
