Binomial Transform Technique for Solving Second Linear Difference Equations
DOI:
https://doi.org/10.29304/jqcsm.2025.17.22216Keywords:
Difference Equations, Second Linear Difference Equations, Binomial TransformAbstract
Our main goal in this research is to study the binomial transformation to solve second-order linear difference equations. It has been concluded that the binomial transformation method is an easy and simple way to solve second-order difference equations after the initial conditions are met.
The research recommended using the binomial transformation to solve partial difference equations.
Downloads
References
. Eman A. Hussain and Asmaa S. Jasim (Binomial Transform Technique For Solving Linear Difference Equations) Journal of Al-Qadisiyah for Computer Science and Mathematics Vol. 13(2) 2021 , pp Math . 193–202
.Ş.Şi¸sman and M. Merdan, On the solution of random linear difference equations withLaplace transform method, Math. Meth. Appl. Sci. 46 (2023), 18258–18273. DOI 10.1002/mma.9556.ŞIŞMAN and MERDAN 18273.
. Bernstein, M. and Sloane, N. J. A. "Some Canonical Sequences of Integers." Linear Algebra Appl. 226/228, 57-72, 1995.
. Khristo N. Boyadzhiev, Binomial transform and the backward difference. Adv. Appl. Discrete Math., 13(1)(2014),43-63.
. Khristo N. Boyadzhiev, Binomial transform of products, Ars Comb., 126 (2016), 415 434.
. K. W. Chen, Identities from the binomial transform, J. Number Theory 124(2007), 142-150.
. Yan-Ping Mu, Symmetric recurrence relations and binomial transforms, J. Number Theory, 133 (2013) 3127-3137.
. Mogens E. Larsen and Peter J. Larcombe, Some binomial coefficient identities of specific and general type, Util. Math., 74 (2007), 33-53.
. N. YÄ´slmaz, N. Taskara, Binomial transforms of the Padovan and Perrinnumbers, Journal of Abstract and Applied Mathematics, (2013) ArticleID941673.
. H. Prodinger, Some information about the binomial transform, The Fibonacci Quarterly, 32(5), 1994, 412-415.
. Boyadzhiev, K. (2018). Notes on the Binomial Transform: Theory and Table with Appendix on Stirling Transform, World Scientific, Singapore.
. Jensen, A. "Lecture Notes on Difference Equations" DK- 9220, Version1, July 18, 2011.
. Jerri, Abdul J.," Linear Difference Equations With Discrete Transform Methods", Kluwer Academic Publishers, 1996.
. Miclcnes,R.E."Difference Equations. Theory Applications and advanced Topics", 3^ed ed. Champam & Hall , 2015.
. Kelley W.G,& Pcterson A.C." Difference Equations. An Introduction with Applications", 2^ed ed .Academic Press , 2001.
. Elaydi, S.N. "An introduction to difference equations" , Springer, 2^ed ed . 1999 .
. L. Brand, A sequence defined by a difference equation, Amer. Math. Monthly 62 (1955), no. 7, 489–492. https://doi.org/https://doi.org/10.2307/2307362
. S. N. Elaydi, An Introduction to Difference Equations, second edition, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1999. https://doi.org/10.3934/ dcdss.2015.8.1055
. K. S. Berenhaut and S. Stević, The behaviour of the positive solutions of the difference equation x_n=A+( x_n-2 x_(n-1)) p , J. Difference Equ. Appl. 12 (2006), no. 9, 909–918. https://doi.org/10.1155/2008/653243
. Miclcnes,R.E."Difference Equations. Theory Applications and advanced Topics",3nd ed. Champam & Hall , 2015.
. X. I. Kartala, N. Englezos, and A. N. Yannacopoulos, Future expectations modeling, random coefficient forward–backward stochastic differ-ential equations, and stochastic viscosity solutions, Math. Oper. Res. 45 (2020), 1–31.
. S. Al-Ahmad, M. Mamat, and R. AlAhmad, Finding differential transform using difference equations, IAENG Int J Appl Math 50 (2020),127–132
. R. Al Ahmad, Finding Laplace transform using difference equations, J. Math. Computer Sci. 23 (2021), no. 2021, 75–79.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Asmaa S. Jasim
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
