Symmetry Lie algebra and exact solutions of some fourth-order difference equations
Volume 11, Issue 11, pp 1262--1270
http://dx.doi.org/10.22436/jnsa.011.11.06
Publication Date: September 05, 2018
Submission Date: October 30, 2017
Revision Date: August 04, 2018
Accteptance Date: August 07, 2018
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Authors
N. Mnguni
- School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.
D. Nyirenda
- School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.
M. Folly-Gbetoula
- School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.
Abstract
In this paper, all the Lie point symmetries of difference equations of the form
\[
u_{n+4}=\frac{u_n}{A_n +B_nu_nu_{n+2}},
\]
where, \((A_n)_{n \geq 0}\) and \((B_n)_{n \geq 0}\) are sequences of real numbers, are obtained. We perform reduction of order using the invariant of the group of transformations. Furthermore, we obtain their solutions. In particular, our work generalizes some results in the literature.
Share and Cite
ISRP Style
N. Mnguni, D. Nyirenda, M. Folly-Gbetoula, Symmetry Lie algebra and exact solutions of some fourth-order difference equations, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 11, 1262--1270
AMA Style
Mnguni N., Nyirenda D., Folly-Gbetoula M., Symmetry Lie algebra and exact solutions of some fourth-order difference equations. J. Nonlinear Sci. Appl. (2018); 11(11):1262--1270
Chicago/Turabian Style
Mnguni, N., Nyirenda, D., Folly-Gbetoula, M.. "Symmetry Lie algebra and exact solutions of some fourth-order difference equations." Journal of Nonlinear Sciences and Applications, 11, no. 11 (2018): 1262--1270
Keywords
- Difference equation
- symmetry
- group invariant solutions
MSC
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