TY - JOUR
T1 - Algebrization of nonautonomous differential equations
AU - Alcorta-García, María Aracelia
AU - Frías-Armenta, Martín Eduardo
AU - Grimaldo-Reyna, María Esther
AU - López-González, Elifalet
N1 - Publisher Copyright:
© 2015 María Aracelia Alcorta-García et al.
PY - 2015
Y1 - 2015
N2 - 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.
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: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.
UR - http://www.scopus.com/inward/record.url?scp=84948659503&partnerID=8YFLogxK
U2 - 10.1155/2015/632150
DO - 10.1155/2015/632150
M3 - Artículo
SN - 1110-757X
VL - 2015
JO - Journal of Applied Mathematics
JF - Journal of Applied Mathematics
M1 - 632150
ER -