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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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/632150 |
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| author | María Aracelia Alcorta-García Martín Eduardo Frías-Armenta María Esther Grimaldo-Reyna Elifalet López-González |
| author_facet | María Aracelia Alcorta-García Martín Eduardo Frías-Armenta María Esther Grimaldo-Reyna Elifalet López-González |
| author_sort | María Aracelia Alcorta-García |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-aa83f6863f344063bafaafba32f0765a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-aa83f6863f344063bafaafba32f0765a2025-02-03T05:52:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/632150632150Algebrization of Nonautonomous Differential EquationsMaría Aracelia Alcorta-García0Martín Eduardo Frías-Armenta1María Esther Grimaldo-Reyna2Elifalet López-González3Universidad Autónoma de Nuevo León, Avenida Universidad, S/N, Ciudad Universitaria, 66451 San Nicolás de los Garza, NL, MexicoDepartamento de Matemáticas, Universidad de Sonora, Boulevard Rosales y Luis Encinas, S/N, Col. Centro, 83000 Hermosillo, SON, MexicoUniversidad Autónoma de Nuevo León, Avenida Universidad, S/N, Ciudad Universitaria, 66451 San Nicolás de los Garza, NL, MexicoUniversidad Autónoma de Ciudad Juárez, Unidad Multidisciplinaria de la UACJ en Cuauhtémoc, Carretera Cuauhtémoc-Anáhuac, Col. Ejido Anáhuac km 3.5, S/N 31600, Municipio de Cuauhtémoc, CHIH, MexicoGiven 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.http://dx.doi.org/10.1155/2015/632150 |
| spellingShingle | María Aracelia Alcorta-García Martín Eduardo Frías-Armenta María Esther Grimaldo-Reyna Elifalet López-González Algebrization of Nonautonomous Differential Equations Journal of Applied Mathematics |
| title | Algebrization of Nonautonomous Differential Equations |
| title_full | Algebrization of Nonautonomous Differential Equations |
| title_fullStr | Algebrization of Nonautonomous Differential Equations |
| title_full_unstemmed | Algebrization of Nonautonomous Differential Equations |
| title_short | Algebrization of Nonautonomous Differential Equations |
| title_sort | algebrization of nonautonomous differential equations |
| url | http://dx.doi.org/10.1155/2015/632150 |
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