TY - JOUR A2 - Leach, Peter G. L. AU - Alcorta-García, María Aracelia AU - Frías-Armenta, Martín Eduardo AU - Grimaldo-Reyna, María Esther AU - López-González, Elifalet PY - 2015 DA - 2015/11/09 TI - Algebrization of Nonautonomous Differential Equations SP - 632150 VL - 2015 AB - 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:ΩR2×R2R2 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. SN - 1110-757X UR - https://doi.org/10.1155/2015/632150 DO - 10.1155/2015/632150 JF - Journal of Applied Mathematics PB - Hindawi Publishing Corporation KW - ER -