On a two-dimensional solvable system of difference equations

Here we solve the following system of difference equations xn+1 = ynyn−2 bxn−1 + ayn−2 , yn+1 = xnxn−2 dyn−1 + cxn−2 , n ∈ N0, where parameters a, b, c, d and initial values x−j , y−j , j = 0, 2, are complex numbers, and give a representation of its general solution in terms of two specially chosen...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerző: Stević Stevo
Dokumentumtípus: Folyóirat
Megjelent: 2018
Sorozat:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet
doi:10.14232/ejqtde.2018.1.104

Online Access:http://acta.bibl.u-szeged.hu/58117
Leíró adatok
Tartalmi kivonat:Here we solve the following system of difference equations xn+1 = ynyn−2 bxn−1 + ayn−2 , yn+1 = xnxn−2 dyn−1 + cxn−2 , n ∈ N0, where parameters a, b, c, d and initial values x−j , y−j , j = 0, 2, are complex numbers, and give a representation of its general solution in terms of two specially chosen solutions to two homogeneous linear difference equations with constant coefficients associated to the system. As some applications of the representation formula for the general solution we obtain solutions to four very special cases of the system recently presented in the literature and proved by induction, without any theoretical explanation how they can be obtained in a constructive way. Our procedure presented here gives some theoretical explanations not only how the general solutions to the special cases are obtained, but how is obtained general solution to the general system.
Terjedelem/Fizikai jellemzők:1-18
ISSN:1417-3875