Analytic solution for telegraph equation by differential transform method. (English) Zbl 1237.35150
Summary: The differential transform method (DTM) is considered to solve the telegraph equation. This method is a powerful tool for solving large amount of problems (see for instance [J. K. Zhou, Differential transformation and its application for electrical circuits (Chinese), Wuuhahn, China: Huarjung University Press (1986); C. K. Chen and S. H. Ho, Appl. Math. Comput. 106, No. 2–3, 171–179 (1999; Zbl 1028.35008); M.-J. Jang, C. L. Chen and Y.-C. Liu, ibid. 121, No. 2–3, 261–270 (2001; Zbl 1024.65093); F. Kangalgil and F. Ayaz, Chaos Solitons Fractals 41, No. 1, 464–472 (2009; Zbl 1198.35222); A. S. V. Ravi Kanth and K. Aruna, ibid. 41, No. 5, 2277–2281 (2009; Zbl 1198.81089); A. Arikoglu and I. Ozkol, ibid. 34, No. 5, 1473–1481 (2007; Zbl 1152.34306)]). Using the differential transform method, it is possible to find the exact solution or a closed approximate solution of an equation. To illustrate the ability and reliability of the method some examples are provided. The results reveal that the method is very effective and simple.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
Citations:
Zbl 1198.81038; Zbl 1198.81089; Zbl 1152.34306; Zbl 1028.35008; Zbl 1024.65093; Zbl 1198.35222References:
| [1] | Zhou, J. K., Differential Transformation and Its Application for Electrical Circuits (1986), Huarjung University Press: Huarjung University Press Wuuhahn, China |
| [2] | Chen, C. K.; Ho, S. H., Appl. Math. Comput., 106, 171 (1999) · Zbl 1028.35008 |
| [3] | Jang, M. J.; Chen, C. L.; Liu, Y. C., Appl. Math. Comput., 121, 261 (2001) · Zbl 1024.65093 |
| [4] | Kangalgil, F.; Ayaz, F., Chaos Solitons Fractals, 41, 1, 464 (2009) · Zbl 1198.35222 |
| [5] | Ravi Kanth, S. V.; Aruna, K., Chaos Solitons Fractals, 41, 5, 2277 (2009) · Zbl 1198.81089 |
| [6] | Arikoglu, A.; Ozkol, I., Chaos Solitons Fractals, 34, 1473 (2007) · Zbl 1152.34306 |
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