### MATHEMATICAL AND NUMERICAL APPROACH FOR TELEGRAPHER EQUATION

#### Abstract

**Abstract:** The well known second order partial differential equation called telegrapher equation has been considered. The telegrapher formula is an expression of current and voltage for a segment of a transmission media and it has many applications in numerous branches such as random walk, signal analysis and wave propagation. In this paper, we first derived the telegrapher equation. As a second step we solved the boundary value problem of telegrapher equation analytically, were we have make use of Fourier series. Finally, the numerical solution for the telegrapher equation for different cases of initial and boundary condition is studied and obtained.

**Key words:** Communications, Telegraph, Differential Equation, Telegraph Equation, Numerical Solution.

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