Z-transform solution for nonlinear difference equations
DOI:
https://doi.org/10.23851/mjs.v32i4.1019Keywords:
difference equations, nonlinear difference equations, Z-transform.Abstract
The aim of this paper is to study Z-transform to solve non-linear difference equations, after converting them to linear difference equations by one of the conversion methods. This is because the z-transform cannot be directly applied to the nonlinear difference equations.
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Roy, S.C.D., Difference Equations, Z-transforms and Resistive Ladders, IETE Journal of Equation, Vol. 52, Issue 1, 2011.
Cochran, W.T., James W. Cooley, D.L.Favin, H. D. Helms, R. A. Kaenel, W .W. Lang, Jr. Maling G. C., D. E. Nelson,C. M. Rader, and Peter D. Welch. 1967. "What Is the Fast Fourier Transform?" Proceedings of the IEEE 55 (10): 1664-74.
Reabiner, L. R., Schafer, R. W. , Rader, C. M.: The Chirp Z- transform Algorithm ,June 1969, IEEE Transactions On Audio And Electroacoustics Vol. Au-17, No. 2.
L. Brand, A sequence defined by a difference equation, Amer. Math. Monthly 62 (1955), no. 7, 489-492.
S. N. Elaydi, An Introduction to Difference Equations, second edition, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1999.
K. S. Berenhaut and S. Stević, The behaviour of the positive solutions of the difference equation , J. Difference Equ. Appl. 12 (2006), no. 9, 909-918.
I. Bajo and E. Liz, Global behaviour of a second-order nonlinear difference equation, J. Difference Equ. Appl. 17 (2011), no. 10, 1471-1486.
M. Dehghan, R. Mazrooei-Sebdani, and H. Sedaghat, Global behaviour of the Riccati difference equation of order two, J. Difference Equ. Appl. 17 (2011), no. 4, 467-477.
Stević, S.: Solvable subclasses of a class of nonlinear second-order difference equations. Adv. Nonlinear Anal. 5(2), 147-165 (2016).
Stević, S.: Solvability of a one-parameter class of nonlinear second-order difference equations by invariants. Adv. Differ. Equ. 2019, Article ID 151 (2019).
S. Stevi'c, M. A. Alghamdi, N. Shahzad, and D. A. Maturi, On a class of solvable difference equations, Abstr. Appl. Anal. 2013 (2013), Art. ID 157943.
On a solvable nonlinear difference equation of higher order, Turkish J. Math. 42 (2018), no. 4, 1765-1778.
D. T. Tollu, Y. Yazlik, and N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Adv. Difference Equ. 2013 (2013), 174, 7 pp.
Y. Halim and M. Bayram, On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences, Math. Methods Appl. Sci. 39 (2016), no. 11, 2974-2982.
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