Algebrization of nonautonomous differential equations

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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, ζ) and H2 (ζ)=H(τ, ζ) are Lorch differentiable with respect to A for all (τ,)ε Ω, where τ and represent variables in A. Under these conditions the solutions (τ) of the differential equation d/dτ=H(τ, ζ) over A define solutions (x(t),y(t))=(te) of the planar system.

Original languageEnglish
Article number632150
JournalJournal of Applied Mathematics
StatePublished - 2015

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© 2015 María Aracelia Alcorta-García et al.


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