A detailed study of a class of recurrence equations with a generalized order

Volume 32, Issue 4, pp 318--331 http://dx.doi.org/10.22436/jmcs.032.04.03

Publication Date: October 26, 2023 Submission Date: February 07, 2023 Revision Date: July 27, 2023 Accteptance Date: August 25, 2023

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 265 Downloads
• 661 Views

Authors

J. T. Kubayi - School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa. M. Folly-Gbetoula - School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa.

Abstract

In this paper, we study some family of difference equations. The study involves the use of symmetries to find exact solutions of difference equations with the aim of extending the studies that have been done in the literature. We also investigate the periodic nature and behavior of the solutions in some cases. Finally, some numerical examples illustrating our findings are presented.

Share and Cite

Keywords

• Difference equation
• symmetry
• reduction
• exact solution

MSC

•  39A10
•  39A99
•  39A13

References

• [1] L. S. Aljoufi, M. B. Almatrafi, A. R. Seadawy, Dynamical analysis of discrete time equations with a generalized order, Alex. Eng. J., 64 (2023), 937–945
  • View Article
  • Google Scholar


• [2] M. B. Almatrafi, Analysis of solutions of some discrete systems of rational difference equations, J. Comput. Anal. Appl., 29 (2021), 355–368
  • View Article
  • Google Scholar


• [3] M. B. Almatrafi, M. M. Alzubaidi, Stability analysis for a rational difference equation, Arab J. Basic Appl. Sci.,, 27 (2020), 114–120
  • View Article
  • Google Scholar


• [4] M. B. Almatrafi, M. M. Alzubaidi, The solution and dynamic behaviour of some difference equations of seventh order, J. Appl. Nonlinear Dyn., 10 (2021), 709–719
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] M. B. Almatrafi, E. M. Elsayed, Solutions and formulae for some systems of difference equations, MathLAB J., 1 (2018), 356–369
  • View Article
  • Google Scholar


• [6] M. B. Almatrafi, E. M. Elsayed, F. Alzahrani, The Solution and Dynamic Behavior of Some Difference Equations of Fourth Order, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 29 (2022), 33–50
  • View Article
  • Google Scholar
  • MATH


• [7] G. C¸ inar, A. Gelis¸ken, O. O¨ zkan, Well-defined solutions of the difference equation xn = xn-3kxn-4kxn-5k xn-kxn-2k(1xn-3kxn-4kxn-5k), Asian-Eur. J. Math., 12 (2019), 13 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] M. Folly-Gbetoula, A. H. Kara, Invariance analysis and reduction of discrete Painlev´e equations, J. Difference Equ. Appl., 22 (2016), 1378–1388
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] M. Folly-Gbetoula, K. Mkhwanazi, D. Nyirenda, On a study of a family of higher order recurrence relations, Math. Probl. Eng., 2022 (2022), 11 pages
  • View Article
  • Google Scholar


• [10] M. Folly-Gbetoula, N. Mnguni, A. H. Kara, A group theory approach towards some rational difference equations, J. Math., 2019 (2019), 9 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] M. Folly-Gbetoula, D. Nyirenda, Lie symmetry analysis and explicit formulas for solutions of some third-order difference equations, Quaest. Math., 42 (2019), 907–917
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] M. Folly-Gbetoula, D. Nyirenda, Explicit formulas for solutions of some (k+3)th-order difference equations, Differ. Equ. Dyn. Syst., 31 (2023), 345–356
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] P. E. Hydon, Difference equations by differential equation methods, Cambridge University Press, Cambridge (2014)
  • View Article
  • MathSciNet
  • Google Scholar


• [14] S. Lie, Vorlesungen ¨uber Differentialgleichungen: Mit Bekannten Infinitesimalen Transformationen, BG Teubner: Leipzig, Germany (1891)
  • View Article
  • Google Scholar
  • MATH


• [15] S. Maeda, The similarity method for difference equations, IMA J. Appl. Math., 38 (1987), 129–134
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] N. Mnguni, M. Folly-Gbetoula, Invariance analysis of a third-order difference equation with variable coefficients, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 25 (2018), 63–73
  • View Article
  • Google Scholar
  • MATH


• [17] N. Mnguni, D. Nyirenda, M. Folly-Gbetoula, Symmetry Lie algebra and exact solutions of some fourth-order difference equations, J. Nonlinear Sci. Appl., 11 (2018), 1262–1270
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] On the solutions and behavior of rational difference equations, Y. Yazlik, J. Comput. Anal. Appl., 17 (2014), 584–594
  • View Article
  • Google Scholar
  • MATH