International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 753916, 21 pages
Research Article

On Solving Systems of Autonomous Ordinary Differential Equations by Reduction to a Variable of an Algebra

1Facultad de Ciencias, Universidad Autónoma de Baja California, Km. 103 Carretera Tijuana-Ensenada, 22860 Ensenada, BC, Mexico
2Grupo Alximia SA de CV, Departamento de Investigación, Ryerson 1268, Zona Centro, 22800 Ensenada, BC, Mexico
3Departamento de Matemáticas, Universidad de Sonora, 83000 Hermosillo, SON, Mexico
4División Multidisciplinaria de la UACJ en Cuauhtémoc, Universidad Autónoma de Ciudad Juárez, 32310 Ciudad Juárez, CHIH, Mexico

Received 26 March 2012; Accepted 16 May 2012

Academic Editor: Mihai Putinar

Copyright © 2012 Alvaro Alvarez-Parrilla et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new technique for solving a certain class of systems of autonomous ordinary differential equations over is introduced ( being the real or complex field). The technique is based on two observations: (1), if has the structure of certain normed, associative, commutative, and with a unit, algebras over , then there is a scheme for reducing the system of differential equations to an autonomous ordinary differential equation on one variable of the algebra; (2) a technique, previously introduced for solving differential equations over , is shown to work on the class mentioned in the previous paragraph. In particular it is shown that the algebras in question include algebras linearly equivalent to the tensor product of matrix algebras with certain normal forms.