Transient analysis of lossless transmission lines

The method of characteristics provides a simple analytic solution for the transient analysis of a uniform, lossless transmission line. The interpretation of this solution in terms of equivalent network of the input and output behavior of the transmission line leads to an efficient algorithm which yields not only the input and output responses but also the incident and reflected waves. This method is superior in both speed and accuracy to the familiar method of integrating the differential equations that describe a lumped LC model of the line; but it is not applicable to lossy lines.