Mathematically Modeling the Telephone and Telegraph Equations in a Long Cable or Transmission Line

Nwakaego S.i, Ehiwario J.c and Dr C.E. Emenonye
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Nwakaego S.i: Department of Mathematics, College of Education, Agbor Delta State, Nigeria
Ehiwario J.c: Department of Mathematics, College of Education, Agbor Delta State, Nigeria
Dr C.E. Emenonye: Department of Mathematics, College of Education, Agbor Delta State, Nigeria

International Journal of Research and Innovation in Applied Science, 2020, vol. 5, issue 8, 39-41

Abstract: This paper presents a mathematical model of the telephone and telegraph equations in a transmission line. The flow of electricity in a transmission line was considered. It was observed that waves and wave propagation are ubiquitous in nature and lead to many puzzling questions. For example, why is it that a storm over the ocean sets off a steady swell of small-amplitude waves, but an earthquake at the sea floor can release an enormous flood wave? What produces mirages in the desert? In response to these questions, a great deal of mathematics has been developed to understand and predict the dynamics of light or sound waves the propagation of matter waves, the vibration patterns of elastic bodies, or the peculiar nature of water waves. This paper will provide a guided tour of mathematical wave theory together with physical applications, including the linear wave equation, dispersion and nonlinear waves and solitons. Mathematically one – dimensional heat equations for the flow were derived.

Date: 2020
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