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


Authors

Darlison Nyirenda - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa. Mensah Folly-Gbetoula - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.


Abstract

We perform a full Lie point symmetry analysis of difference equations of the form \[ u_{n+6}=\frac{u_nu_{n+4}}{u_{n+2}(A _n + B _n u_nu_{n+4})}\ , \] where the initial conditions are non-zero real numbers. Consequently, we obtain four non-trivial symmetries. Eventually, we get solutions of the difference equation for random sequences \((A_n)\) and \((B_n)\). This work is a generalization of a recent result by Khaliq and Elsayed [A. Khaliq, E. M. Elsayed, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 1052--1063].


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ISRP Style

Darlison Nyirenda, Mensah Folly-Gbetoula, Invariance analysis and exact solutions of some sixth-order difference equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6262--6273

AMA Style

Nyirenda Darlison, Folly-Gbetoula Mensah, Invariance analysis and exact solutions of some sixth-order difference equations. J. Nonlinear Sci. Appl. (2017); 10(12):6262--6273

Chicago/Turabian Style

Nyirenda, Darlison, Folly-Gbetoula, Mensah. "Invariance analysis and exact solutions of some sixth-order difference equations." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6262--6273


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