Modified Numerical Technique for the Solution of the Telegraph Equation

Author : Mohammad H. Al-Towaiq, Tamem Y. Al-Shorman

Abstract :The telegraph equation describes the voltage and current on an electrical transmission line with distance and time. � �2𝑢 𝑑𝑥2 with the initial conditions: =𝛼𝑑2𝑢 𝑑𝑡2 +𝛽𝑑𝑢 𝑑𝑡 +𝛶𝑢 � �(𝑥,0) = 𝜙1(𝑥) , 𝑢𝑡(𝑥,0) = 𝜙2(𝑥) and the boundary conditions � �(0,𝑡) = 𝜓1(𝑡) , 𝑢𝑥(0,𝑡) = 𝜓2(𝑡) where 𝞪, 𝞫 and 𝜰 are positive constants and 𝜙1(𝑥),𝜙2(𝑥),𝜓1(𝑡),and 𝜓2(𝑡) are continuous functions. In this paper, we introduce a numerical solution for the one-dimensional telegraph equation based on the finite difference scheme. The numerical results show the applicability, efficiency, and accuracy of the method compared with other methods.

Keywords :Numerical Analysis, Mathematical Modeling, Operations Research

Conference Name :International Conference on Discrete Applied Mathematics and Parallel Processing (ICDAMPP -25)

Conference Place Kuala Lumpur, Malaysia

Conference Date 28th Feb 2025