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

Alvaro Alvarez-Parrilla, Martín Eduardo Frías-Armenta, Elifalet López-González and Carlos Yee-Romero

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-21

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:753916

DOI: 10.1155/2012/753916

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