Simulation of the Propagation of Electromagnetic Oscillations by the Method of the Modified Equation of the Telegraph Line


  • R.L. Politansky Yuri Fedjkovych Chernivtsy National University
  • Z.M. Nytrebych Lviv Polytechnic National University
  • R.I. Petryshyn Yuriy Fedkovych Chernivtsi National University
  • I.T. Kogut Vasyl Stefanyk Precarpathian National University
  • O.M. Malanchuk Danylo Halytsky Lviv National Medical University
  • M.V. Vistak Danylo Halytsky Lviv National Medical University



telegraph line, two-point problem


The article considers the physical processes associated with the propagation of electromagnetic oscillations in a long line, the size of which is the same or slightly greater than the length of the electromagnetic wave (not more than ten times). As a research method, the differential-symbolic method is used, which is applied to the modified equation of the telegraph line. The boundary conditions for the two-point problem as well as additional parameters that are coefficients for the first derivatives in terms of coordinate and time in comparison with the classical equation of the telegraph line are considered as parameters for controlling the process of propagation of electromagnetic oscillations. Based on the differential-symbolic method, the boundary conditions of the two-point problem are found, under which the most characteristic oscillatory processes are realized in a long line. Based on the research, it is possible to draw conclusions about the effectiveness of analytical methods for the analysis of specific technical objects and control of the processes that take place in them.


R. Politanskyi, M. Klymash, 2019 3rd International Conference on Advanced Information and Communications (Lviv, 2019), p. 390 (

Y. Bobalo, L. Nedostup, M. Kiselychnyk, M. Melen, Computational Problems of Electrical Engineering (CPEE), 17th International Conference (2016), p.1 (

S.D. Galiuk, M.Y. Kushnir, R.L. Politanskyi, 21st International Crimean Conference^ Microwave and Telecommunication Technology (2011), p. 423.

A. Veryga, R. Politanskyi, V. Lesinskyi, T. Ruda, 15th International Conference on Advanced Trends in Radioelectronics, Telecommunication and Computer Engineering (Lviv-Slavske, 2020), p. 162 (DOI: 10.1109/TCSET49122.2020.235414).

Y. Bobalo, M. Kiselychnyk, L. Nedostup, Przegląd Elektrotechniczny 86, 124 (2010).

Z. Mykytyuk, G. Barylo, V. Virt, M. Vistak, I. Diskovskyi, Y. Rudyak, International Scientific-Practical Conference on Problems of Infocommunications, Science and Technology (Kiyv, 2018), p. 177 (

O. Sushynskyi, M. Vistak, V. Dmytrah, 13th International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science (Lviv-Slavske, 2016), p. 418 (

Z. Hotra, Z. Mykytyuk, I. Diskovskyi, G. Barylo, F. Vezyr, 14th International Conference on Advanced Trend in Radioelectronics, Telecommunications and Computer Engineering (Lviv-Slavske, 2018), p. 716 (

R.L. Politanskyi, M.V. Vistak, G.I. Barylo, A.S. Andrushchak, Optical Materials 102, 109782 (2020) (

I.T. Kogut, V.I. Holota, A.A. Druzhinin, V.V. Dovhij, Journal of Nano Research 39, 228 (2016) (

K. Narahara, Journal of Applied Physics 100(6), 064908 (2006).

K. Narahara, T. Yamaki, T. Takahashi, T. Nakamichi, International Journal of High Speed Electronics and Systems 17(3), 577 (2007).

H. Shanak, O. Florea, N. Alshaikh, J. Asad. Acta Technica Napocensis, Ser.: Applied Mathematics and Engineering 63, 143 (2020).

M. Dehghan, A. Ghesmati, Eng. Anal. Boundary Elem. 34(1), 51 (2010).

M. Dehghan, A. Shokri, Numer. Methods Partial Differ. Equ. 24, 1080 (2008) (

A. Ashyralyev, M. Modanli, Boundary Value Problems 41, 1 (2015) (

Z. Nytrebych, O. Malanchuk, Italian J. of Pure and Appl. Mathematics 41, 242 (2019).

Z. Nytrebych, O. Malanchuk, J. Math. Sci. 227, 68 (2017).

Z. Nytrebych, O. Malanchuk, Demonstratio Mathematica 52(1), 88 (2019) (https://

Z. Nytrebych, O. Malanchuk, Asian-European Journal of Mathematics 12(3), 1950037 (2019) (



How to Cite

Politansky, R., Nytrebych, Z., Petryshyn, R., Kogut, I., Malanchuk, O., & Vistak, M. (2021). Simulation of the Propagation of Electromagnetic Oscillations by the Method of the Modified Equation of the Telegraph Line. Physics and Chemistry of Solid State, 22(1), 168–174.



Scientific articles

Most read articles by the same author(s)