The invariance and formulas for solutions of some fifth-order difference equations
Authors
M. Folly-Gbetoula
- School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.
D. Nyirenda
- School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.
Abstract
Lie group analysis of the difference equations of the form
\[
x_{n+1} =\frac{x_{n-4}x_{n-3}}{x_{n}(a_n +b_nx_{n-4}x_{n-3}x_{n-2}x_{n-1})},
\]
where \(a_n\) and \(b_n\) are real sequences, is performed and non-trivial symmetries are derived. Furthermore, we find formulas for exact solutions of the equations. This work generalizes a recent result in the literature.
Share and Cite
ISRP Style
M. Folly-Gbetoula, D. Nyirenda, The invariance and formulas for solutions of some fifth-order difference equations, Journal of Mathematics and Computer Science, 29 (2023), no. 2, 131--141
AMA Style
Folly-Gbetoula M., Nyirenda D., The invariance and formulas for solutions of some fifth-order difference equations. J Math Comput SCI-JM. (2023); 29(2):131--141
Chicago/Turabian Style
Folly-Gbetoula, M., Nyirenda, D.. "The invariance and formulas for solutions of some fifth-order difference equations." Journal of Mathematics and Computer Science, 29, no. 2 (2023): 131--141
Keywords
- Difference equation
- symmetry
- reduction
- group invariant solutions
MSC
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