Algebrization of Nonautonomous Differential Equations

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...

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Bibliographic Details
Published inJournal of Applied Mathematics Vol. 2015; no. 2015; pp. 770 - 779-075
Main Authors María Aracelia Alcorta-García, Martín Eduardo Frías-Armenta, María Esther Grimaldo-Reyna, Elifalet López-González
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 2015
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Wiley
Subjects
Algebra
Associative
Differential equations
Functions (mathematics)
Mathematical analysis
Ordinary differential equations
Partial differential equations
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Summary: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.
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ISSN:1110-757X
1687-0042
DOI:10.1155/2015/632150