Algebrization of Nonautonomous Differential Equations. (9th November 2015)

• Record Type: Journal Article
• Authors: Alcorta-García, María Aracelia; Frías-Armenta, Martín Eduardo; Grimaldo-Reyna, María Esther; López-González, Elifalet
• Other Names: Leach Peter G. L. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2015(2015)
• Publication Date: 2015-11-09
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2015/632150
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : Given a planar system of nonautonomous ordinary differential equations, d w / d t = F ( t, w ), conditions are given for the existence of an associative commutative unital algebraA with unite and a functionH : Ω ⊂ R 2 × R 2 → R 2 on an open setΩ such thatF ( t, w ) = H ( t e, w ) and the mapsH 1 ( τ ) = H ( τ, ξ ) andH 2 ( ξ ) = H ( τ, ξ ) are Lorch differentiable with respect toA for all( τ, ξ ) ∈ Ω, whereτ andξ represent variables inA . Under these conditions the solutionsξ ( τ ) of the differential equationd ξ / d τ = H ( τ, ξ ) overA define solutions( x ( t ), y ( t ) ) = ξ ( t e ) of the planar system.