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

Author

Listed:
  • Alvaro Alvarez-Parrilla
  • Martín Eduardo Frías-Armenta
  • Elifalet López-González
  • Carlos Yee-Romero

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.

Suggested Citation

  • Alvaro Alvarez-Parrilla & Martín Eduardo Frías-Armenta & Elifalet López-González & Carlos Yee-Romero, 2012. "On Solving Systems of Autonomous Ordinary Differential Equations by Reduction to a Variable of an Algebra," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-21, October.
    • Handle: RePEc:hin:jijmms:753916
    DOI: 10.1155/2012/753916
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    References listed on IDEAS

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    1. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
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