The problem of voltage in a bounded telegraph line with periodic voltage perturbation at the left end

Goryunov Alexander Vladimirovich, Kostikov Yuri Alexandrovich, Prokofiev Alexander Ivanovich, Romanenkov Alexander Mikhailovich

The paper considers the telegraph equation, which is an important special case for the Maxwell equation for current propagation through wires. The solution of the telegraph equation is the distribution function of the electric voltage in a bounded wire. An original method for obtaining an exact solution of a boundary value problem with a nontrivial boundary condition is proposed. A series of auxiliary functions was introduced, which made it possible to reduce to the classical one-dimensional problem of string oscillation with Dirichlet conditions at the ends of the wire. By the method of separation of variables, an exact solution was obtained in the form of a convergent Fourier series.

Keywords:telegraphic equation, boundary value problem, exact solutions