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.

Abstract

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.