On a Study of a Family of Higher-Order Recurrence Relations

Folly-Gbetoula, Mensah; Mkhwanazi, Kgatliso; Nyirenda, Darlison

doi:10.1155/2022/6770105

Cited by 3 publications

(2 citation statements)

References 23 publications

(59 reference statements)

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“…and demonstrate how one uses the solution of (1.3) to recover those of (1.1). For more results on difference equations, the reader can refer to [2][3][4][5][6][7][8]10] 1.1. Preliminaries.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of Thirtieth-Order Difference Equations

Thomas,

Folly-Gbetoula

2024

Int. J. Anal. Appl.

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The main goal of this paper is to determine exact solutions of a family of thirtieth-order difference equations with variable coefficients. We use similarity variables obtained via symmetries to lower the order of the equations. We then reverse the transformations and obtain closed form solutions. We compare our solutions to those found in the literature for special cases. We investigate the periodic nature of the solutions and present some numerical examples to confirm the results. Finally, we analyze the stability of the equilibrium points. The method employed in this work can be applied to equations of higher order provided that they admit non zero characteristics.

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Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of Thirtieth-Order Difference Equations

Thomas,

Folly-Gbetoula

2024

Int. J. Anal. Appl.

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“…and presented the formula for solutions as well as their asymptotic behavior. For similar studies on difference equations of this form, the reader can refer to [5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Solutions of Higher-Order Difference Equations

Folly-Gbetoula

2023

Mathematics

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The invariance method, known as Lie analysis, consists of finding a group of transformations that leave a difference equation invariant. This powerful tool permits one to lower the order, linearize and more importantly, obtain analytical solutions of difference and differential equations. In this study, we obtain the solutions and periodic solutions for some family of difference equations. We achieve this by performing an invariance analysis of this family. Eventually, symmetries are derived and used to construct canonical coordinates required for the derivation of the solutions. Moreover, periodic aspects of these solutions and the stability character of the equilibrium points are investigated.

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