The Dynamics and Solution of some Difference Equations

Khaliq, Abdul; Elsayed, E. M.

doi:10.22436/jnsa.009.03.33

Cited by 12 publications

(8 citation statements)

References 3 publications

(3 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, by using a symmetry based method, we have obtained a solution of a more general form of the difference equations considered in [9]. Thus we studied difference equations of the form…”

Section: Resultsmentioning

confidence: 99%

“…, and obtained their solutions. It should be noted that Khaliq and Elsayed [9] considered the cases with all possible combinations of A n ∈ {−1, 1} and B n ∈ {−1, 1}, and our case goes beyond the ±1 setting by generalizing the situation to (B n ) and (A n ) being non-zero sequences of real numbers.…”

Section: Resultsmentioning

confidence: 99%

“…When this method is employed, we expect single solutions with fewer constraints on initial conditions. Our work is inspired by the results of Khaliq and Elsayed [9] where the following difference equation was studied x n+1 = x n−1 x n−5 x n−3 (±1 ± x n−1 x n−5 )…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Invariance analysis and exact solutions of some sixth-order difference equations

Nyirenda¹,

Folly-Gbetoula²

2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Invariance analysis and exact solutions of some sixth-order difference equations

Nyirenda¹,

Folly-Gbetoula²

2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

show abstract

“…, n ∈ N 0 , (1.4) where k ∈ N, which is a natural generalization of the equations given in [10,11,14,20,21]. On the other hand, in [1], Eq.…”

Section: Introductionmentioning

confidence: 99%

Solvability of a system of nonlinear difference equations of higher order

Kara¹,

Yazlık²

2019

Turk J Math

View full text Add to dashboard Cite

In this paper, we show that the following higher-order system of nonlinear difference equations, xn = x n−k y n−k−l y n−l (an + bnx n−k y n−k−l) , yn = y n−k x n−k−l x n−l (αn + βny n−k x n−k−l) , n ∈ N0, where k, l ∈ N , (an) n∈N 0 , (bn) n∈N 0 , (αn) n∈N 0 , (βn) n∈N 0 and the initial values x−i, y−i , i = 1, k + l , are real numbers, can be solved and some results in the literature can be extended further. Also, by using these obtained formulas, we investigate the asymptotic behavior of well-defined solutions of the above difference equations system for the case k = 2, l = k .

show abstract

“…Van Khuong and Phong (2011) investigated the difference equation −3 = (1 + −1 −2 ), = 0,1, . ... Khaliq and Elsayed (2016) Suppose that I is some interval of real numbers and F a continuous function defined on I k+1 (k+1 copies of I), where k is some natural number. Throughout this thesis, we consider the following difference equation…”

Section: Introductionmentioning

confidence: 99%