The initial-boundary value problem for transmission line equations

In this thesis the initial-boundary value problem for the transmission line problem is investigated. As it is known that the transmission line (or telegraph) equations are first order partial differential equations. For these system of equations both exact and numerical solutions are obtained.In the first section, in order to find the solution of the transmission line equations necessary basic concept are given too. It is known that the telegraph equation is second order. Moreover the solution of the second order equation of hyperbolic type is continuous but the first order derivatives of the solution with respect to x is discontinuous function on the along characteristics. Since the classical solution of this problem does not exist, the concept of the weak solution and some notions associated with it are given.In the second section, the definition of the hyperbolic type equation and the characteristics are investigated.In the third section, on basis of the suggested auxiliary problem the exact solution of model of the nonlinear differential equation of hydrodynamics is obtained.Finally, the Riemann invariants of the transmission line equation are found. Besides, the simple algorithm for the numerical solution of the transmission line equations in a class of discontinuous function is developed.