An Efficient Computational Technique for the Analysis of Telegraph Equation

Selim Hussen; Mahtab Uddin; Md. Rezaul Karim

doi:10.38032/jea.2022.03.005

Authors

Selim Hussen Department of Mathematics, Chittagong University of Engineering and Technology, Chattogram-4349, Bangladesh
Mahtab Uddin Institute of Natural Sciences, United International University, Dhaka-1212, Bangladesh
Md. Rezaul Karim Department of Mathematics, Jagannath University, Dhaka-1100, Bangladesh

DOI:

https://doi.org/10.38032/jea.2022.03.005

Keywords:

Damping Coefficient, Transmission Velocity, Time Propagation, Voltage Drop, Pulse Height, COMSOL Multiphysics, Numerical Simulation

Abstract

The Telegraph equation has drawn much attention due to its recent variety of applications in different areas of the communication system. Various methods have been developed to solve the Telegraph equation so far. In this research paper, we have formulated a derivation mathematically for the Telegraph equation for the section of a line of transmission concerning the voltage associated and the current. Therefore, obtained mathematical equation has been solved numerically by COMSOL Multiphysics. We have then numerically analyzed the parametric behavior of the Telegraph equation. The analysis first starts with allowing both the damping coefficients to vary, keeping the transmission velocity fixed, and observing the pulse shape at different time slots. We have then investigated the deformation of the pulse caused due to the gradual increase of transmission velocity for varying damping coefficients at the intended discrete time slots. Finally, we analyzed the behavior of the associated voltage pattern for those variations due to the corresponding distance of the Telegraph wire. We have observed that changes in the damping coefficients have a gradual impact on the associated voltage of the Telegraph equation, which is more conspicuous for the higher time slots. Transmission velocity is found as the most influential parameter of the Telegraph equation that controls the deformation of the pulse height, which is the cardinal part of the inquiry.

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