Algebrization of Nonautonomous Differential Equations

María Aracelia Alcorta-García, Martín Eduardo Frías-Armenta, María Esther Grimaldo-Reyna and Elifalet López-González

Journal of Applied Mathematics, 2015, vol. 2015, issue 1

Abstract: Given a planar system of nonautonomous ordinary differential equations, dw/dt = F(t, w), conditions are given for the existence of an associative commutative unital algebra A with unit e and a function H:Ω⊂R2×R2→R2 on an open set Ω such that F(t, w) = H(te, w) and the maps H1(τ) = H(τ, ξ) and H2(ξ) = H(τ, ξ) are Lorch differentiable with respect to A for all (τ, ξ) ∈ Ω, where τ and ξ represent variables in A. Under these conditions the solutions ξ(τ) of the differential equation dξ/dτ = H(τ, ξ) over A define solutions (x(t), y(t)) = ξ(te) of the planar system.

Date: 2015
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https://doi.org/10.1155/2015/632150

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2015:y:2015:i:1:n:632150

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