Article
The Form of the Solutions and Periodicity of Fourth Order Recursive Sequence
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Abstract
We obtain, in this paper the solution of the following difference equation $x_{n+1} = \frac{x_{n-1}}{x_{n-3}(x_{n-1} \pm 1)}$, $n = 0,1, \dots$, where the initial conditions $x_3, x_2, x_1, x_0$ are arbitrary non zero real numbers. Also we study the periodicity of the solutions of these equations.
Keywords
Solutions and Periodicity, difference equation, fourth order recursive sequence
Citation
Alayachi, H. S., Noorani, M. S. M., & Elsayed, E. M. (2022). The form of the solutions and periodicity of fourth order recursive sequence. Numerical and Computational Methods in Sciences and Engineering, 4(2), 49–58. https://doi.org/10.18576/ncmse/040202
H. S. Alayachi, M. S. M. Noorani and E. M. Elsayed, “The form of the solutions and periodicity of fourth order recursive sequence,” Numerical and Computational Methods in Sciences and Engineering, vol. 4, no. 2, pp. 49–58, 2022, doi: 10.18576/ncmse/040202.
Alayachi HS, Noorani MSM, Elsayed EM. The form of the solutions and periodicity of fourth order recursive sequence. Numerical and Computational Methods in Sciences and Engineering. 2022;4(2):49–58. doi:10.18576/ncmse/040202.
Alayachi, H. S., Noorani, M. S. M. and Elsayed, E. M. (2022), ‘The form of the solutions and periodicity of fourth order recursive sequence’, Numerical and Computational Methods in Sciences and Engineering, 4(2), pp. 49–58. Available at: https://doi.org/10.18576/ncmse/040202.
Alayachi, H. S., et al. “The Form of the Solutions and Periodicity of Fourth Order Recursive Sequence.” Numerical and Computational Methods in Sciences and Engineering, vol. 4, no. 2, 2022, pp. 49–58. https://doi.org/10.18576/ncmse/040202.
Alayachi, H. S., M. S. M. Noorani, and E. M. Elsayed. “The Form of the Solutions and Periodicity of Fourth Order Recursive Sequence.” Numerical and Computational Methods in Sciences and Engineering 4, no. 2 (2022): 49–58. https://doi.org/10.18576/ncmse/040202.
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