Acceleration techniques have been incorporated into the generalized method of characteristics (GMC) to perform transient analysis of uniform transmission lines, for the special case when the transmission lines are driven by digital signals. These techinques have been proved to improve the simulation speed to a great extent when the analysis is carried out using iterative waveform relaxation method. It has been identified that the load impedance connected to the transmission line has a bearing on the efficiency of one of these acceleration techniques. Examples of an RLCG line terminated with linear loads as well as nonlinear loads are given to illustrate the advantage of incorporating these acceleration techniques.