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Dynamics and Solutions of Higher-Order Difference Equations

Author

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  • Mensah Folly-Gbetoula

    (School of Mathematics, University of the Witwatersrand, Johannesburg 2000, South Africa)

Abstract

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.

Suggested Citation

  • Mensah Folly-Gbetoula, 2023. "Dynamics and Solutions of Higher-Order Difference Equations," Mathematics, MDPI, vol. 11(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3693-:d:1226777
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    References listed on IDEAS

    as
    1. L. Ndlovu & M. Folly-Gbetoula & A. H. Kara & A. Love, 2014. "Symmetries, Associated First Integrals, and Double Reduction of Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, July.
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