A complete mathematical model of power transmission lines is obtained for time and space dependent shunt parameters and time dependent series parameters. All possible initial and boundary conditions related with line terminations are tabulated. The nonlocal boundary value problem for the resulting telegraph equation is considered and numerical solutions of this problem are computed by using various finite difference schemes. Errors in the numerical solutions and the relevant central processing unit (CPU) time spent for processing are presented. The problem is also solved by using perturbation-iteration algorithm (PIA). The results are compared with each others and the advantage or disadvantage of any method is discussed. Second-order difference method and third-order difference method are applied for solving one-dimensional telegraph equation used for power transmission lines in the case of open-circuit ended and short-circuit ended. The results about the voltage responses of all cases are discussed.