Solve the Hanoi Puzzle Using Difference Equations

Authors

  • Hamza M. Salman AL-qasim Green University
  • Huda Amer Hadi University of Babylon

Keywords:

Difference Equations. Homogenous first order Linear Difference Equations.Higher order Linear Difference with constant coefficients.

Abstract

This research aims to solve an old riddle invented by the French mathematician (Edward Lucas) in the year 1883 AD, known as ( Tower of Hanoi puzzle) using difference equations, which we will address in terms of its concept, some characteristics, types, methods of solving each type of them and some illustrative examples.

References

Mickens, R. E. (2015). Difference equations: theory, applications and advanced topics. CRC Press. .

Jagerman, D. L. (2000). Difference equations with applications to queues. CRC Press .

Berg, L. (2004). Inclusion theorems for non-linear difference equations with applications. Journal of Difference Equations and Applications, 10(4), 399-408..

Lv, Z., Liu, Q., & Wang, P. (2012). Literatures review on transaction costs measurement advances. Asian Social Science, 8(12), 127-132.

Kelley, W. G., & Peterson, A. C. (2001). Difference equations: an introduction with applications. Academic press.

Alzabut, J., Abdeljawad, T., & Baleanu, D. (2018). Nonlinear delay fractional difference equations with applications on discrete fractional Lotka–Volterra competition model. J. Comput. Anal. Appl, 25(5), 889-898.

Meleshko, S. V., Moyo, S., & Oguis, G. F. (2014). On the group classification of systems of two linear second-order ordinary differential equations with constant coefficients. Journal of Mathematical Analysis and Applications, 410(1), 341-347.

Onitsuka, M. (2017). Influence of the stepsize on Hyers–Ulam stability of first-order homogeneous linear difference equations. Int. J. Difference Equ, 12(2), 281-302..

Jivulescu, M. A., Napoli, A., & Messina, A. (2008). General solution of a second order non-homogenous linear difference equation with noncommutative coefficients. arXiv preprint arXiv:0804.2792.

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Published

2022-12-19

How to Cite

Hamza M. Salman, & Huda Amer Hadi. (2022). Solve the Hanoi Puzzle Using Difference Equations. International Journal of Scientific Trends, 1(3), 15–23. Retrieved from https://scientifictrends.org/index.php/ijst/article/view/30

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